Prop 13 means that property taxes on residences in California cannot increase more than 2% per year. It also mandates that reassessment cannot happen unless ownership changes hands or significant construction is done (such as tearing down the house and building something else).
Basically, the longer you own a house in California, the lower your effective property taxes are.
But your main point is correct: A more productive use of the land would be for grandma to sell her home to a developer who would then build apartments. Reassessing property taxes every few years is a great way to encourage such developments. Again, the end result isn't to take someone's home. It's to tax them commensurate with the value of the land (a scare resource in cities). If they don't think the taxes are worth it, they can sell their land (usually for millions of dollars) and move to a place where land isn't as expensive.
I don't think the neighbors want apartments either. That would instantly crater the desirability of the neighborhood. This matters both for the people concerned about finances and for the people who just want to live their lives in peace.
You can't just move a really old person without increasing the risk of death. She would lose her connections to church and family. She would lose the familiarity of her home, both inside and out. This would likely cause depression and might even cause confusion.
If we're going to be coveting land, what about the park? The land value of Golden Gate Park is immense. People wanting a park can go visit one where the land isn't as expensive.
Basically, the longer you own a house in California, the lower your effective property taxes are.
But your main point is correct: A more productive use of the land would be for grandma to sell her home to a developer who would then build apartments. Reassessing property taxes every few years is a great way to encourage such developments. Again, the end result isn't to take someone's home. It's to tax them commensurate with the value of the land (a scare resource in cities). If they don't think the taxes are worth it, they can sell their land (usually for millions of dollars) and move to a place where land isn't as expensive.