Is there wide agreement it is misbehaving and ought to be changed “somehow”? Perhaps it could be modified.
There are other ways to achieve the basic objective without creating the same side effects. For example, Colorado’s TABOR has a very similar objective with a very different mechanism that slows property tax growth but does not pressure people to stay put in their current home.
> Is there wide agreement it is misbehaving and ought to be changed “somehow”?
No, voters overwhelmingly support Prop 13 in general, and feel that property taxes (which in fact are extremely low by national standards due to the Prop 13 nominal rate limit even before considering the Prop 13 assessment increase limit) are high in California. (What's actually high is property values, as a result of both Prop 13 and development policy -- and the development policy is itself, in part, due to incentives created by Prop 13 which align with those created by homeowner NIMBYism.)
It has been tweaked before, and you could maybe pass tweaks again that would enhance revenue in general, but by and large the basic structure is going to be very hard to change.
Prop 13 has been modified several times since being passed; its not impossible that it would be modified in a way which would increase overall property tax revenue, but procedurally its basically impossible for that to be relevant to the short-term funding shortfall.
I think a modification that separately tracked the prop 13 basis and a current price and charged taxes on the current price for anything that isn’t the owner’s primary residence could plausibly tax — after all, no one would get priced out of their own home as a result.
There are other ways to achieve the basic objective without creating the same side effects. For example, Colorado’s TABOR has a very similar objective with a very different mechanism that slows property tax growth but does not pressure people to stay put in their current home.