Your tax burden would stay the same, relative to future buyers, if prices stay flat. At which some point, they're bound to plateau. How many people or institutions will buy single family homes once they're $10 million each, but the median household income is still somewhere around $100k? It's a subtle point, but the benefits of Prop 13 aren't a function of time, they're a function of appreciation. It just so happens to be the decades following Prop 13 came with great price appreciation, some of that attributable to Prop 13 itself, but most of it attributable to local rule of land use policy.

I think inflationary monetary policy (a good thing) more or less guarantees that in dollar terms (the thing that matters for prop 13) prices will go up every year. I think prop c does allow for some price adjustment for inflation, but it has a crazily low cap

Property taxes can go up 2% per year. That's reasonable from an inflation perspective if you are just living there. (Supposedly inflation has been that low for a long time, but doesn't feel like it in real cost of living)

I think you need to defend your claim that inflationary monetary policy is a good thing. How is it good for the residents of a country?

I mean to the best of my knowledge basically all economists think it is, but beyond that imagine a world where we had stagnation or worse deflation. You would have much less of an incentive to invest money rather than just keep it in the bank.