If your whole neighborhood goes up, but not the whole city/municipality, correct. If the entire tax base goes up (not just one neighborhood), you should expect the mill rate to fall.

Does it actually, though?

In practice - aren't tax rates changed based on politics?

Tax rates are generally changed by an independent political process (the municipal budget) which often has the power to increase/decrease the mill rate based on how much money is needed/desired. This doesn't change the fact that the mill rate does generally fall by a lot when properties are reassessed in areas that have seen a large property price increase.

This is not the case where I live. Levy rates are set in statute.

Are rates proportional to house valuations used in “most places in the U.S”?

That is, are most rates not “mill rates” (where relative house values matter, not absolute values).

Yeah I'm very curious about this. I assumed that because my taxes have been purely proportional in the several places that I've lived that this was generalized to across the U.S.

This is the first I've heard of a city adjusting taxes down.