Because people don't enjoy paying taxes if they perceived they should go down.

The cost of running a city is largely independent of house prices, so if the real estate market crashes there is no getting around that municipalities need to increase tax rates to meet their cashflow needs. People may not like that they feel they are getting ripped off, but the existing infrastructure has relatively fixed ongoing costs to maintain.

Oh absolutely, but that ignores the political cost of doubling tax rates.

Better to not get into that mess to begin with. Strongtowns is a great resource for cities looking to be prudent financially.