You're forgetting that their property taxes are continuing to go up even though property values have gone down significantly. Why? Because their assessed value is below market value and as long as that's true, their taxes go up.
That factor makes property tax revenues far less volatile than they would be otherwise.
We know what counties and cities do when property tax revenues boom without a cap - they ramp up their spending. When property values crash, as they do every decade or so, that tanks their revenue, so cities and counties jack up the rates.
> If you are a new resident though, you get no immediate benefit - your taxes are assessed at the purchased value.
You get the benefit of knowing how your property taxes will behave. (If you buy right before a crash, you do get a respite until values recover.)
> that's $17.6 billion a year - pretty much the budget deficit of the state.
It's also significantly less than state spending has increased in the last few years. Note that the state isn't supposed to get property tax revenues - they're collected by cities and counties.