It's a pretty weak argument. You could simply report your dependants on a form and then the IRS can use that for a calculation.
Sure. And on that same form you can also report all of the other details they might not have, like whether you bought an EV or installed home efficiency upgrades that qualify for a tax credit, and what charitable donations you made that are tax deductible, and what your state and local taxes are, and... you get the point. Just to be sure, maybe you should also include the details you're sure they do have. And given that there's some ambiguity in the law about how some of this stuff fits together as well as some choices you get to make, maybe you could also do the calculations.
You've just reinvented the 1040.
We frequently in american say something is impossible when it's trivial to solve or every other country has already solved it.
This one is completely solvable, but the place you have to start is not with the forms and flow of information, the place you have to start is the tax code and the laws regulating what other entities have to report, and are allowed to report.
For example, consider state and local taxes. Two options: Either you eliminate the state and local tax deduction on federal income taxes or you require all state and local tax entities to report your payments to them. This also means that all of those entities have to have a way to uniquely identify you. We abuse the social security number (which was not intended to be used as an identifier for anything except the social security program) for this, and that's probably fine in this case, though it's also possible that the Privacy Act restricts it in some cases, so the law might have to be tweaked there, too.
For the charitable donations case, same options: Either eliminate the tax deduction or require all charities to report donations, which will require you to give your social security number to them. I'm not sure how people would feel about having to provide their SSN to Goodwill when they drop off some old furniture.
Same with EV. If you want to keep the tax credits, auto dealers will have to report to the IRS. At least you already more or less have to give them your SSN.
Same with energy efficiency upgrades, except that's complicated by the fact that some people buy the units themselves and install them, so Home Depot et al have to begin reporting to the IRS, and you have to give them your SSN, while other people hire a contractor, who will have to do the reporting, and to whom you'll have to provide your SSN.
And so on across the hundreds, perhaps thousands, of other issues.
Yes, most people don't have any of these other issues in a given year (except state and local taxes), so a compromise might be a simple system for people who just have W-2 income and take the standard deduction, and no other complications. It's hard to see how it could be simplified for anyone with more complex taxes, though, unless the tax code was overhauled to simply eliminate all of the deductions and credits.