I've sinced developed a more nuanced view. I believe Prop13 for owner-occupied, primary residences is perhaps flawed, but something I believe two reasonable people can disagree on (happy to explain more fully). I believe Prop13 for anything else has absolutely no rational justification and needs to be overturned at the earliest opportunity.
Secondly, I contend that the limit should never have been on the amount of tax levied, only on the amount of tax that actually had to be paid in a given year. The locality would receive a lien on the balance which would be paid only when the property was sold. (The lien could also be capped at 1/3 the selling price, to answer objections that it might become so large as to make it uneconomic to sell the property at all. I suggest this because whenever I float this proposal on HN, someone comes along and fixates on that possibility, which is actually extremely unlikely; the market would have to tank very severely for this cap to come into play.)
This way, fixed-income seniors could stay in their homes just as long as Prop. 13 allows them to, but localities would still get their money.