Property tax is on the one hand a wealth tax, which sounds like a great idea; but on the other hand, it's a wealth tax that disproportionately affects people with the bulk of their assets tied up in real estate --- which often means middle class homeowners.
So while you can certainly look at prop 13 as "good" in that folks don't get priced out of their existing homes, it of course gets used to the advantage of rent seekers, etc.
Property tax is on the one hand a wealth tax, which sounds like a great idea;
The problem is in how its assessed. A market-based tax will be vulnerable to market manipulation. A tax accessed by the agents of lobbyists and kleptocrats will be administered to the benefit of their patrons.
This isn't a policy failure quite so much as it is a democratic failure.
Yeah, without being a policy junkie I think a reasonable step would be to have Prop 13 only apply to primary residence --- investment real estate would be subject to a "wealth tax," but folks wouldn't get priced out of their primary home due to gentrification.
Prop 13 should also not apply to inherited houses. It's creating a class of landed gentry who were lucky enough to have parents living near the housing boom, and pricing out anyone who moved here in the last 20 years.