Two claims in my post:

1) > They're pretty much the only capital city in the developed world that's a burden and not a benefit to the country as a whole.

https://www.iwkoeln.de/presse/iw-nachrichten/matthias-dierme...

2) > Then they do things like free daycare paid for by other states in the country while those states can't offer it.

Look up "Länderfinanzausgleich" and then look up daycare programs and compare them. None of the net payers get even remotely the same even though they're the ones actually paying for it.

Both statements are objectively true.