My parents were in a very similar situation, with dad still living.
Governor Jerry Brown back in the 1970’s got a law passed that taxes the home off the original purchase price, not a yearly to market markup.
This is also why when people buy scrapers, they tear out the roof and 3 walls, leaving just bare concrete and one wall. That way when they do their 3000 ft addition, it’s still taxed off the original purchase price.
People don’t move within CA because they can’t afford the move. That’s why they move out of state.