That's not what Prop 13 is about, it treats golf courses and property speculation the same as people on disability or pensions. It treats vacation homes and investment property the same way.
If it was about keeping at-risk people in their homes, there would be some mention of that. If it were about that, Prop 13's effect would be mostly to keep at-risk people in their homes. But the majority of what Prop 13 does is reward the super wealthy and jack up the incentives for speculation on real estate. Compare the tax incentives handed out to the wealthy compared to those tax incentives given to those in need, is there any chance that Prop 13 is meant for those at need?
Be honest here, does a Howard Jarvis tax bill sound like something aiming at helping those in need, or is the "help" just a cover for a scheme to hugely increase wealth inequality, and force larger tax burdens away from the wealthy to the less wealthy?
So don't give us those false accusations that wanting to fix the horribleness of Prop 13 means wanting to kick people out of their homes, those two concepts are not connected.
Why should taxes be disproportionally higher for new buyers and housing options more limited for everyone else? Not everyone in the world can live in California, and I'm not convinced that living there decades ago entitles you to live there forever if you can't afford the current prices. As a society we've decided to allocate scarce resources by price. If someone bought property in California decades ago and can't afford to pay their fair share of taxes on that property now, they can sell it at a huge increase in price and can afford to buy a luxury property in most other areas of the country.