Many (most?) people in the US pay their taxes by withholding, which comes out of each paycheck. But if not, quarterly payments are generally required. You can make payments monthly if you like, but for determining if payments were timely, they'll be aggregated by quarters.

> I always wondered why giant tax jurisdictions never try to just do one single non-micro-optimized tax rate ladder across everyone and zero other taxes / deduction / special regimen etc.

All the wacky deductions and special credits and what not are implementation of economic policies. Credits encourage behavior, and taxes discourage it. For some, a paperwork burden is enough to discourage behaviors.

> France collects directly from salary, so now there's no tax return for the vast majority of tax payers, it's a bit riskier since you can't escape it, but... can't do much simpler.

The US does withholding, but it's not necessarily correct for many reasons; some good, some bad. If income tax was a flat rate with no deductions, withholding would be enough. But other sources of income, such as bank interest or stock sales, usually don't have withholding, so you'd need to pay those taxes separately. And your employer may not know about your spouse's income, etc. And, people like getting a refund, even it doesn't make fiscal sense.