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...
As far as I know, my area doesn’t do that. The assessments go up over time, but there’s no large jump on transfer of ownership.
The hand-wavy explanation is that in the late 70's when this initiative passed (Prop 13), home values were rising rapidly due to an influx of people moving to the state and higher inflation rates of the times. Many people that owned homes, including those that had purchased their homes and retired, were getting priced out of their homes on the property tax rates. There are other rationales or rationalizations depending on where you come down on it. But Prop 13 was intended to slow property tax growth while you owned the property, with assessment reset to full market value at sale time.