Fyi if all properties increase equally in value and municipal costs remain the same, so do your taxes.
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.