Those who would benefit from its repeal - renters, people who moved out, people who choose not to move to CA in the first place because of cost and governance, children, etc, either don't vote as consistently or can't vote in CA at all.
Proposition 15 (which would have eliminated commercial property tax breaks) failed 48%-52%. I think its biggest political flaw is probably the fact that it would apply July 1, 2022, with no phase-in for small businesses whose lease passes through the property tax. So hopefully in November 2022 another attempt can be made that addresses the political shortcomings.
Proposition 19 (which eliminated tax breaks for inherited investment property in exchange for increased tax portability for the elderly) only barely passed 51%-49%, and that was after it received overwhelming support from the legislature, and a $45 million advertising campaign from the California Association of Realtors that some people criticized for only highlighting the goodies for old people and not the costs for inheritors.
No one is attempting a full repeal of Proposition 13 including residential property.
It could also be attacked judicially; see this episode of the Henry George Program for a discussion of Nordlinger v Hahn and whether different legal arguments could be tried (e.g. does Proposition 13 impinge on the American freedom to migrate under the US Constitution?) http://seethecat.org/ep/2017-07-11.html
I believe it could be revisited on the grounds that Prop 13 primarily benefits white families (makes sense -- they were the only ones buying property 40 years ago).
There is now good data on the racial disparities in our current tax law and with enough money I think another lawsuit has a chance.
https://twitter.com/alfred_twu/status/1327821019931787264?s=...
People don't move because there's a tax hike proportionate to how long you've lived there, so there's less turnover in housing, meaning less supply, meaning higher prices.
It puts a hard, long term, effectively permanent cap on tax growth, so cities must plan for everything to continually get leaner. Cities make land use and zoning decisions based on uses that are net contributors to revenue, vs net costs. What is a net cost? Housing in general, especially housing that might contain school aged children - that's why 3+ bedroom apartments are so much more rare. What are net contributors? Offices and retail. So the places with demand get to pick, and SF and the Peninsula restrict housing as much as they can and have a huge concentration of offices.
Places on the outskirts (e.g. Dublin, Livermore, Gilbert, Brentwood) are allowing housing to be built because they're trying to turn nothing into something, but any established, and especially built-out city, has a strong financial incentive not to admit a single additional resident to live there, while encouraging everyone they can to shop and work there.