Property tax itself is not the issue. The issue is caps on property tax increases that are meant to protect those poor fixed income people. Essentially, people do not make any change that would require the property to be reassessed, which may massively increase the taxes to where they should be. Hence people not doing some minor addition.
But those rules are specific to California? I'm confused why people seem to be suggesting that a land value tax is the only possible solution, when an alternative would be to just make taxes in that state work the same as elsewhere.
California is not unique in capping property tax increases in that way. Other states do it. California has a uniquely bad law though since the capped prices can be passed on to family. I agree that LVT is not the only way to fix those issues but LVT has some other benefits as well (such as discouraging empty lots).