Worth remembering that this is already pretty much the law in California. Under Propositions 19, 90, 110, 58, 193, and 60, the state allows seniors and some other groups to carry their low assessment to a new property.
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The interesting thing here is that in some senses this was an improvement because the general freeze on assessments from Prop 13 made moving a huge fiscal loss, which discouraged sales, which could actually reduce property taxes for local govs.
Yep and this is one of the biggest reasons why CA is so f*cked. Local control has eroded ever since most of our tax dollars go to the state.