Yes, that is indeed how things work. It is not part of the budget and the ruling coalition has no mandate to bargain with it. I believe most European countries have similar checks and balances in place. I do not understand what the contradiction is, but if there is one it must be widespread.

We pay for many things we can not use, roads where we don't live, schools we can not attend and health care for the opposite sex. That does not mean public funding is good in itself, only that the grey area between what is public and what is private is large and politicized and settled over time. I disagree with many of them but that is no reason to get counterfactual.

There was a loud public debate about the migration crisis, both at the time and for a long time afterwards. It is important to recognize these things even if we don't personally agree with the outcome. That's part of living in a democracy.