Ah, that’s a nice breeze you’ve got going there, with all that handwaving. Could you turn a little to the left? My ear’s getting a little warm, from all the bullshit being piped into it.
You want to see absurdity crystallized? Here it is: “haircuts… there is going to be someone who will do it at no cost”. Why in the everloving world do you think that people are going to want to cut your hair for free? For the thrill of running their fingers through your glossy locks? Okay, let’s suppose that there are some people so enraptured with the glorious art of their haircuts that they will do it just for the art of it. I’d be terrified to put myself under their scissors, not being the guinea-pig type for somebody’s artistic rapture, but okay. So, how many of these people are there? A few thousand, on the entire planet? You wanna travel three thousand miles and stand in line for six months to get a haircut?
Now let’s talk about those people who will do plumbing for free for the artistic thrill of fitting pipes. And the police and sanitarium guards who do it for the sheer thrill of enforcing justice through club and gun. (Okay, you could probably find plenty of people like that, so long as you don’t interfere with them with annoying moral limitations on their behavior.) And then of course there are all those experts who are doing hard work as full time judges - though again, there are probably enough people who like being controlling, manipulating, and power-mad to fill those slots.
Here’s where you made your error: you’re trying to pretend that humans can participate in your society, when there’s a much easier answer for you: sentient robots with supermagic AIs. Sentient robots give all the haircuts, do all the guarding, make all the decisions, give all the advice, provide all the casual sex, and provide all the companionship. Only these godlike silicon beings, who will have been flawlessly programmed to all be selfless altuistic angels by God himself, only they can be relied upon to act as the cogs of a functioning society.
Obviously somebody’s been reading some sci-fi. Though apparently only a limited selection - the robots turn evil or go loopy in at least half of those stories, largely because it makes for a more interesting plot. Heck, even Asimovian robots with the three laws go bad half the time!
But anyway, back to the idealized super-robot-run society: what are we actually talking about here? We’re talking about humans having been almost completely removed from functional society. Certainly, humans can’t be tasked with doing anything that needs to be done - the human could easily decide to quit and go home any time things get a little hard (since you’re not paying him). So all necessary tasks of any kind must be done by the sentient robots that will permeate society, most likely in numbers exceeding humanity itself (since everyone will always want at least one robotic slave handy).
So, what do humans do in this society? Well, humans have shown a limited inclination to do creative endeavors for no pay. Most of stuff so created is crap, mind you - the artistic community will be dominated by Mary Sues and other quick throwaway work. Presumably there will still be some art of scope and quantity created, though. I suspect much of it will never be distributed to a general audience - if you’ve put a lot of effort into something and care about it, you may not want to see it taken and mocked or (worse) modified by the hack down the street, painting penises on your masterpeice. But there will surely be some who are both skilled and interested enough in the mere acclaim of the faceless masses to expose their work to the world, so human art will not be completely dead.
Plus of course, we can reasonably expect the robots to be creating art too - they’re creative and imaginative enough to govern everything, so it makes sense they could create art too. Presumably better art than any human, since we’ve already assumed the robots are perfect and godlike.
So anyway, some humans will be spending their time creating art for public consumption - assuming they feel that they’re not totally outclassed and shamed by the robot art, anyway. What else will humans do? Well, not work obviously; there’s no job we wouldn’t rather give to the robot, so we wouldn’t let people work. (You’ve explicitly said that human labor is valueless anyway - my haircuts are crap, my advice is crap, everything I could do is crap, according to your thesis.) So, what would people do? Laze around their houses, presumably, doing nothing of importance. Most people will get fat and slothful. And associating with other people? People hurt other people. And you’ve got all these much-nicer, kinder, angelic robots around - so who needs people? My robobuddy gives me all the companionship and sex and love I need.
I’d expect the majority of humanity to die off peacefully within three generations, having failed to reproduce. Those that remain will likely have a religious aversion to robot companionship, possibly taking it so far as to reject the robots entirely. Luddiite enclaves might spring up, taking increasingly strident cultural measures to encourage their youth to remain in the fold and actually put up with and reproduce with other human beings. Possibly they might actually declare war on the robots and attempt to destroy them - though I would expect the robots (who would vastly outnumber the humans by that point) to be able to passively let the humans attack and simply replace damaged robots as fast as the humans can destroy them. This is of course assuming that the robots don’t decide the humans would be better off dead, or decide that the spotted owls would be better off if the humans would dead, or decide that the robots would would better off if the humans were dead.
Of course, if the humans all die (one way or the other), then the dream will finally be achieved: a civilization composed entirely of perfectly unselfish, constructive, generous individuals, who will all voluntarily work together in perfect harmony forever. As an added bonus, they’re immune to the effects of disease and aging, too! Perfect! And all it will take is stupidly impossible fantasy made-up AI robots to achieve this end. Surely, that glorious new world will be upon us any day now.