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I bought my house (in CA) in 2019, and my property tax bill is ~$30k/yr. My literal nextdoor neighbor's property tax bill is less than $1k/yr (it last sold in the 1960s and has been passed down within the same family).

And to fix the problem, they added Prop 90 and 19, which now let you transfer the base value around! What an amusing shell game.

https://www.boe.ca.gov/prop19/#FAQs

But more efficiently shuffling existing supply doesn't create new supply.

Tax deferral to the estate for anyone over X age or that has owned a property for more than Y years. Or some gradient on either age or property ownership duration would address some of the issue. Even if you mitigate things with some kind of blanket exemption either of the estate or just to for life for a small set of folks that qualify, you need to stop it from new homeowners getting locked in.