I live in neighbouring Luxembourg now and here it's very simple: public transportation inside the country are free. No need to register or anything: you just hop in and it's free. For tourists, for expats/residents/natives: doesn't matter, it's all free.
Income tax goes as high as 40% in Luxembourg (for the high earners) but it sure seems like people here do get a lot in return for their taxes.
Luxembourg is effectively only offering local/metro level free transit, since the country is tiny. Germany, on the other hand, has regional trains criss-crossing the country that are also free. Yes, the faster IC trains aren't included, but slower trains that go quite far are included.
So, while Germany is indeed charging rather than making them free, they're also offering more than Luxembourg is.
The further trains go, generally the more expensive tickets are, because you get fewer economies of scale compared to local trips within a metro area, and infrastructure upkeep is probably more expensive for such long trips through more remote areas.
* not the fast ones, but still
more like people there get a lot in return for other people taxes...
for private people it isn't
except it is because if you have a very high amount of money you can do all kind of tricks to reduce you personal income (on which you pay high tax) without actually losing out on much, e.g. by having a company have this income instead of you, and you just happen to have 100% control of the company ;=)
for money you spend on private exp-endures of luxury there is often a limit on how much you can trick around so you still have to pay yourself out a not so small amount of money as income and in turn Luxembourg still get a nice amount of tax.
(Edit: Legal tax avoidance of very wealthy people, works roughly like this pretty much everywhere, not just Luxembourg.)
It's really not hard for it to provide free public transportation. (Berlin considered doing it and it's a comparatively poor city). Generally in such small countries a lot of thing are just way easier to implement, through other things are way harder.
Or in other words for many metrics comparing very small countries with non very small countries makes often no sense as the dynamics involved are just too different.