A better argument is "distributing the tax burden based on how long somebody's family has owned property in the same place has a large number of negative effects."

One (of many) serious problem(s) with Prop 13 is that it removes an important feedback mechanism whereby inflating property values result in higher taxes which gives even those who currently own property a financial incentive to support policies that keep housing prices in check. With that feedback mechanism removed, a property-owning homo economicus's rational move is to support policies that drive property values sky high (e.g. very restrictive residential zoning to limit competition while simultaneously seeking intense commercial growth to boost demand) at the expense of other members of the community (e.g. renters and future generations), and that's exactly what has happened in California over the last several decades.

It's not just more taxes. It's that Prop 13 effectively means your taxes go down over time. This encourages people to stay in housing units as long as possible. It also creates a big divide between people who bought early and those actually supporting the government through up-to-date tax rates. Most sickeningly is that privileged tax status can be passed parents and children, effectively creating a separate caste of people with lower taxes.

> Most sickeningly is that privileged tax status can be passed parents and children, effectively creating a separate caste of people with lower taxes.

Thankfully this was significantly curtailed by 2020's Proposition 19.

The taxes are skewed towards the rich, but also towards people who want to move for work. It's a wealth transfer towards the asset rich and immobile from the workers and the mobile. It's the economic distortion that's the problem as much as the lower taxation, but certainly part of it is shifting the taxes even more heavily onto the high income earners.