Another factor in Canada is the ability to attribute some costs and deductions to either spouse - charitable receipts, tax credits for registered savings plans, etc. I assume the same goes for the USA?
For example, I can income-split retirement income with my wife. last year I did so, resulting in her paying slightly more tax, so as to keep my income below the threshold for repaying unemployment insurance, which made the total bill less.
What we see is that all sorts of programs are added to the tax code to appease this or that lobby. Perhaps the USA is not as ludicrous as Canada, which discussed or has (I think, never used most of them?) deductions for fitness/medical, transit, daycare, elder or disabled care, carbon tax, property tax, retirement savings and carry-over, … the list goes on. That does not even take into account the complexities of people who buy and sell items to generate capital gains on a regular basis, or the even more complex issues of rental properties.
Here, and I presume in the USA, if all you do is earn a salary (tax deducted at source) and maybe have a tax-deductible registered retirement savings, then the “send a bill” option would work. The risk is that the most needy would perhaps miss out on deductions not fully covered by reporting (child care? Medical expenses?).
If there’s an item in the tax code, it’s there to encourage a behaviour or save someone with a lobby group some money.
Plus, where you’ve made an obvious error on the form, the tax people will helpfully send you a bill or a refund based on their calculations. If you miss something because you forgot to report it… well, the tax people might figure it out, might not.