There is an idea of excluding commercial properties from Prop 13 too (I think they shouldn't have to be covered to begin with, the whole idea of prop 13 was to "keep that old lady in her house when she has retired and cannot keep up with raising expenses").
Also props 58 and 193 allow to inherit Prop 13 tax assessment by children and grandchildren (again against original idea of prop 13 to just help elderly with living in their places when retired) so Prop 13 expanded that way to became multi-generational.
We can consider excluding non-primary residences from it too.
But if that isn't the case, then wouldn't a home have to be sold to cover the tax increase? So you couldn't keep a home in the family, either.
Also why new homeowners not inheriting it are supposed to be paying property taxes in full?
this would mean proposing that the law that's supposedly meant to help old people would actually be limited to those old people
I'm much more in favor of incentivizing people to support positive change than just bringing out the big sticks. How about giving everyone in the neighboorhood a property tax credit if they vote to upzone? Or giving companies big tax breaks if they allow 50% of their workforce to work remotely (tackling both housing and transportation issues)?