> If we let property taxes just be whatever they "should" be without penalizing home-buying in the process you could at least know what you'd be paying rather than having to factor in a 3-5x increase.

I wouldn't be surprised to hear this varies by jurisdiction. In CA, which has large property tax jumps on sales thanks to Prop 13, it seems like you can know the annual property taxes in advance. The sale price is the taxable valuation* and you can find what the local tax rate is (or you can infer it pretty closely from another recently sold home's public municipal taxes paid).

So solves one problem, but is still problematic :)

*I assume this is the general case, anyways; maybe there's details I'm forgetting about separate tax rates on the land and the improvements; the split of the overall proper value between those two categories was mystifying when I bought...