[thaumasiotes]

> Even if state police are federally funded, why does that matter?

It matters quite a bit to the question of whether federally funded police would ever be allowed. You stated outright that they weren't.

> The use of that funding is still under the power of the state (or else it would be unconstitutional, for the federal government to direct how state institutions are operated).

The normal way in which federal funding operates is that they direct its usage. You're not compelled to do what they want, but if you don't, they don't give you the money.

[DiscourseFan]

When I said "allowed," I meant at a mass scale, at every level, uniformly in a centralized system, not some funds for specific purposes here and there. Now, certainly, there have been times when that sort of federal funding has been specifically intended to more centralize policing in the US, but in general the structure of the state is such to prevent that, unless there is a serious change to US law.