The image of 90 year old widows being forced out of their home was how prop 13 was passed so...

Lot of other states have laws that either cap or defer property taxes for retired people. Not much reason California couldn't do the same.

Prop 13 would be fine if it only applied to retirees over the social security retirement age, and did not pass down the basis to their children.

Ah, duh! I'm so dumb. If only the rest of us were smart enough to think of these simple and fair solutions ourselves :)

Or abolish property taxes and fund cities with consumption taxes or some other tax

Property taxes are a consumption tax on the property that you occupy. Even better, the land portion of the property tax can also be considered a Pigovian tax because it is a tax on the natural resources that you are depriving others of occupying.

A more generic tax would be a wealth tax. Don't tax real estate at all; instead, tax net worth.

However, if all you have is a house in an area with rapid price growth, this change won't save you.

Presumably it would "save" you because your end tax would still be lower (as people whose multi-million dollar homes comprise only a fraction of their wealth would subsidize you). It's a bad idea for a bunch of other reason, though.

The "not saving" part is because if your house appreciates in taxable value - no matter, house tax or whole person worth tax - you have to pay more, and if all you have is the house itself (plus something which generated enough value to pay tax when house was cheaper) then your expense grows without your income. Even if you would comparatively pay less tax than your neighbor.

Land tax is among, if not the most equitable tax there is.