Not every state has something like Prop 13… in a lot of places, taxes did NOT drop significantly because of lower home values, and valuations are sometimes not even based on purchase price.
(NYC does it by equivalent rent, I believe, some NJ towns use a similar formula to come up with an artificial number based on land area, sq ft, and amenities — i.e. one bath is worth x dollars — which is then multiplied by a millage multiplier.)
Really, the inflexible system in CA is CA’s own fault, though I’m reaping the benefits so I shouldn’t whinge about it.