Not nearly regulated highly enough for me. One new regulation I might install is “No business can spend more 1% of its capital on finding ways to game the regulation system.”
In a modern corporate economy, there are so many variations of how people get compensated, I would submit that “wage worker” isn’t really a pillar of capitalism. Yes, many employees get paid an hour wage for an hour of work. Many professional services workers like me get paid a flat salary (plus bonus). Other people have different comp structures.
The important thing is that in a capitalist economy, ideally workers have options for employers based on their skills and abilities, and the ability to quit and go somewhere else as conditions warrant.

In a modern corporate economy, there are so many variations of how people get compensated, I would submit that “wage worker” isn’t really a pillar of capitalism. Yes, many employees get paid an hour wage for an hour of work. Many professional services workers like me get paid a flat salary (plus bonus)
A flat salary is, in this sense, a wage: you put in work for a given period of time, and the entity who directs and supervises your work gives you a set payment for this period of work. Even the bonus is something that is given to you as a payment by your boss.
Contrast that with an independent crafter, who is selling the product of their labor directly to consumers, and who gets all the fruit of their labor themselves.
The corporation is a key point: the corporation, not the worker, owns the means of production, and the corporation functions by taking part of the value of the labor for its shareholders. An independent crafter doesn’t do that. A coop or a guild takes part of the value of the labor, but it puts it back into assisting the crafter, not taken to enrich the owners of the corporation.

So, the government decides how much fish anyone can catch?
In modern societies, which are large enough to need governments, yes. This is extremely common, for both fishing classed as “recreational” (though it may be feeding friends and family) and for commercial fishing. Governments also decide how many deer, how many turkey, and considerably etcetera. There are way too many of us to allow free-for-alls: that wipes out species. The relative free-for-all of open ocean is currently doing a whole lot of damage.
Ancient societies generally had social regulations serving the same purpose. Sometimes, especially when they were relatively newly arrived in the area, they may have wiped out species before they learned how to live in that place.

Profit-seeking is more than just monetary rewards, it involves capital accumulation - the re-investing of the profits into further engines of profit. To me, that’s one of the fundamental characteristics of capitalism.
Yeah. Capitalism is when the money itself – the capital – earns money.

I think the profit motive is covered by #2 self interest.
Self-interest isn’t necessarily in money. It can be in goods (food, housing, clothing, musical instruments, etc.); it can be in societal respect; it can be in time available to do things that don’t, in the given society, bring in any money; it can be in one’s health. I’m sure I’m leaving things out.

The “high percentage of wage labor” aspect is not something that is specific to capitalism. In pretty much any form of government or economics, you will have more people doing actual work than directing the work.
Some people direct their own work. Different societies have different percentages of people doing this.

I assumed that unless people were slaves they worked for wages in basically every system. It’s just their bosses or how the wages were determined that changed.
Nope. There are still quite a few people working for themselves; though in the USA and I’m sure elsewhere many of them have been driven out of business by large corporations. In some areas, as @MrDibble says, this was done by taking the land and resources necessary for people to support themselves, by force, deception, and/or by taking charge of the laws of property rights so that those who don’t have the “right” modern paperwork are allowed no claim.
Our own society used to have a lot more people working for themselves; and while many of them did hire others, those others were often working temporarily for themselves until they learned enough and had accumulated enough resources to set up on their own; or to take over or enter into partnership at the places where they’d started as wage labor, as the previous proprietors grew older.
And there have been many societies that didn’t have wage labor at all in anything remotely resembling the modern sense. People worked for their own (generally extended) families, and/or for community networks of various sorts. Money was for long-distance trades, which were a small percentage of what most people needed.

I assumed that unless people were slaves they worked for wages in basically every system.
No. They could work for themselves, or for a share of the common profit, or for other methods of compensation.

doesn’t even a feudal serf get paid for their labor
No. They laboured as a form of tax, really. And they paid their lord rent. They might earn money from the labour they did for themselves the rest of the time, but they were not paid for the time they worked the lords’ lands.
In any case, I think someone should only only considered a wage labourer when they freely sell their labour for money (or kind) on a contractual (formal or informal) basis to an employer. Various discussions of wage labour expand the concept to anyone who gets paid for their work, but for me, the category “wage labourer” should be confined to workers who have some autonomy to freely enter the labour contract, and do so for an employer.
This is a clear category of worker separate from others such as serfs or the self-employed, and deserves its own label in a discussion such as this. “Wage labourer” is a pretty clear one, that you kind of have to actively mangle in order to fit almost all workers throughout history, when most workers were not hired hands - being either conscripted in various ways, or else subsistence farmers or self-employed.
In any case, I’ve been quite clear what I mean by “wage labourer”, explaining more than once in this thread, so I’m going to consider any more nitpicking of my usage to be disingenuous, going forward, and will treat it as such.

Many professional services workers like me get paid a flat salary
That still makes you a wage labourer.
But my plumber is not a wage laborer. Arguably, neither is my cleaning lady. They both work for themselves, selling their services to a variety of different people, setting a price for the work they do.
I myself am living the socialist dream. A basic income that covers all necessary expenses and then some, plus a job I work because I want to, not because I have no choice but to sell my labor for a wage in order to just barely survive.
I wish more people could have this kind of freedom.

setting a price for the work they do.
That’s tricky, isn’t it? I mean, do they set the price, or does the market set the price?

But my plumber is not a wage laborer. Arguably, neither is my cleaning lady. They both work for themselves, selling their services to a variety of different people, setting a price for the work they do.
Well, no. They are still wage laborers. What makes people wage laborers is that they are paid a market wage for their service. It doesn’t matter if they work for themselves or an employer or through a third party intermediary. The plumber and the cleaning lady are still bound by the going rates for their services.
I would argue that an investment banker or real estate broker are not wage laborers. The real estate broker earns a commission based off the value of their sales and the majority of the banker’s comp is tied to how much value they generate through their deals.
Although interestingly enough, all these people manage to hold down jobs in the same economic system.
I guess I’m having trouble envisioning what would be an example of a system where non-slave employees don’t get paid. Communists pay the workers too. They just have different mechanisms for setting the rates.
There’s a jury wide variation the fees different contractors charge to do the same work around a house. My neighbors paid 50% more than i did to get their leaves cleaned up, and my yard is slightly larger.
Does the market set a range for their fees? No doubt. But they set their own price for their labor within that range. And they might charge me more or less than they charge my neighbor.

But my plumber is not a wage laborer.
“Wages” in the anarcho communist worldview and philosophy does not have the same meaning as rational people use.
The rest of us are hampered in this debate as one person is using a set of definitions that has nothing to do with real world economics. It’s like playing a game of monopoly but one person has their own set of rules.
Just like property, which is not theft.
What we really need is an anarcho-syndicalist commune. We take it in turns to be a sort of executive officer for the week, but all the decisions of that officer have to be ratified at a special bi-weekly meeting by a simple majority in the case of purely internal affairs, but by a two thirds majority in the case of…
I believe that the only world we are now capable of creating without capitalism is one like Ursula LeGuin’s novel Always Coming Home. In that book, humanity has nearly but not quite destroyed itself with capitalism/war/technology, and when it began reconstituting itself, it went with a much earlier model of society. Not utopian, but also, without any reference to what we now think of as civilization.
For one thing, it is much, much, much smaller. Human scale.

They are still wage laborers. What makes people wage laborers is that they are paid a market wage for their service. It doesn’t matter if they work for themselves or an employer or through a third party intermediary. The plumber and the cleaning lady are still bound by the going rates for their services.
It can make a whole hell of a lot of difference to the conditions of the job, as well as sometimes to the pay.
The self-employed person sets their own conditions. The market may indeed limit this somewhat; but there’s nobody telling them ‘you’re going to be fired if you refuse to deal with this customer’ or ‘you must work these specific hours even though there’s nothing about the job that requires it’ or ‘you must wear these clothes to work’ or ‘you must work in the same room with this particular other employee’.
When I sell at farmers’ market, I am in multiple ways in a significantly different position than the person at the checkout at BigBox.
The self-employed person also takes the full payment. The person doing the same job for wages only gets a portion. Having said that – the self-employed person gets no benefits they don’t pay for themselves; and has to do all portions of the work, including the marketing/sales end and, depending on the job, sometimes considerable other work. That may or may not cancel out.
And the self-employed are not “bound by the going wage”. If we price too high for crappy quality we may get no takers, sure. But the price somebody else is getting for a similar good or service (it’s rarely exactly the same) is only one of the factors that goes into setting prices. If I think my tomatoes are worth more, I’ll price them higher. If I can get people to taste one, many of them will pay it. Some of them won’t; so it goes.
Some jobs in the modern world can’t in practice be done by one person, or a small partnership. Others can.

I guess I’m having trouble envisioning what would be an example of a system where non-slave employees don’t get paid.
Getting paid doesn’t make you a wage laborer. I’m repeating myself: very many people used to work for themselves, and some of us still do.
And there certainly used to be systems in which most work was done by family groups for themselves with some exchange with the rest of the community that wasn’t based on money at all; money or some equivalent was for very limited uses and rarely necessary for day to day needs. I don’t know how many of them still survive. They may only work with relatively small groups; but they’re certainly not unimaginable.

Getting paid doesn’t make you a wage laborer. I’m repeating myself: very many people used to work for themselves, and some of us still do.
And see- look at what ararchocommunism bogus “definitions” have brought us to- arguing about what is "wages’, about the “commons”, etc, instead of doing what the Op asked?
And IMHO- the answer is NO, but I think the answer may lie in modified not pure capitalism, like the Nordic nations have- Socialism, Democracy, happy people, and yes- capitalism.

But my plumber is not a wage laborer. Arguably, neither is my cleaning lady.
Are they freely entering into a contract with you to be paid hourly/daily/monthly for work they do for you? Then they’re wage labourers.
The plumber would not be a wage labourer if he was the owner of the plumbing company and he employed the actual guys who snaked your drains, as is the case with my plumber.
“Works for themselves” as I’ve been using it to distinguish from wage labourer, means people who sell the output of their labour, not the labour itself. Like a baker or a potter. Or @thorny_locust at the market.
I get the difference in definitions, but what is the functional difference between, say, an independent plumber and independent baker, for the purpose of this discussion?
Moderating
Coy references to “someone” in the thread is a good way to get a warning.
Knock that shit off.
I’m not warning anyone, yet, but don’t do it again.

Are they freely entering into a contract with you to be paid hourly/daily/monthly for work they do for you? Then they’re wage labourers.
He enters into a contract to fix my sink. For most jobs, the minimum fee meant to cover his time getting to my house covers the actual work, too. And we negotiate when he shows up, but he chooses his tools, the manner in which he does the work, and other “employment” details. As @iiandyiiii says, i don’t see a lot of functional difference between him and an independent baker.

And see- look at what ararchocommunism bogus “definitions” have brought us to- arguing about what is "wages’, about the “commons”, etc, instead of doing what the Op asked?
I don’t see how we can discuss what happens after capitalism without having some ideas of what we mean by capitalism. So these definitions seem helpful to me. Then we can say, well, with this view of capitalism, these other economic strategies might emerge. But with that view of if capitalism, only those things might replace it.