As it is now, the tax rate is set basically based on how long you’ve owned your property. I could be making $$$ and pay very very little. While my neighbor who bought more recently but earns less pays more. This seems deeply unfair to me.
Prop 13 also creates a very volatile tax base for local governments, contributing to the frequent budget issues we see in CA.
Means testing property taxes might make them more volatile than in states that don’t do that, but I can’t imagine it’s worse than the current situation.
Additional prop 13 sets up incentives so homeowners at all income levels are discouraged from selling and moving. And discouraged from allowing more housing supply because they only benefit from increasing housing costs. Taxes that go up with home value tend to blunt some of the benefit of that increasing value.