One difficulty is that it's easier to pass a tax break through a budget process than to pass an equivalent "handout" through a separate one.
For example, in France if you have more than 3(?) kids, you get 70% off all train rides. That required this whole process to get set up (I imagine it was more through regulation than law but you at least need the budget to the SNCF).
The easiest way to get an equivalent thing through the US legal bureaucracy would be to do: "If you send us receipts of your train tickets and have over 3 kids, we'll deduct them from your taxes at 70%".
It "pays for itself" in the sense that the government doesn't have to give money to Amtrack, just give back money that was just given to it by the taxpayer. It doesn't require intergovernmental coordination, just the IRS. It can be passed through the huge budget process. Much easier than many other regulatory schemes.
Well, yes. For instance, Finland, where I live, has a very much simplified income tax collection procedure. Deductions for people with children have been eliminated. Deductions for mortgages are being eliminated. All this in the name of simplicity and, yes, fairness.
After all, if you can afford a mortgage, you are clearly well-off, so you should be taxed more.
(And there is a good point: Mortgage deductions distort the housing market. But rent subsidies distort it even more.)
As opposed to the other countries with automated taxes, that don't attempt it?