If they don't change the tax
rate, and my home doubles in appraised value, my tax liability on the property doubles. True, the city
might reduce tax rates if property values explode like that but they might also just continue to take in the revenue. ¯\_(ツ)_/¯ Another example of why its good to be active in local politics.
FWIW, I live in Texas so this place gets a good chunk of its tax revenue from property taxes. The odds of them cutting the tax rate just because your house shot up in cost at least to me seems pretty low. This is one of the problems of gentrification, where long time owners find they are unable to continue owning in the $90k house they bought 20 years ago because now they pay property taxes on a $750k property.