Unproductive assets like real estate should not be enablers of generational wealth.
Property taxes are weird as they are basically one of the few taxes that continue to happen even without any transactions. Almost all other taxes happen when there is a transaction. For example sales tax, when you buy something; Income tax when you get paid; Tariffs when something is imported ect... Property taxes can also can increase without you doing anything so if your income is fixed or does not increase fast enough you could lose your house due to a tax lien.
If your worried about generational wealth that's why we have inheritance and estate taxes. The federal estate tax can get as high as 40%. However, a home is a productive asset if people are living in it. It may not be as productive as some other uses of property like running a business from it, farming the land ect...
Like I said, you won't lose your house within your lifetime at current property tax rates. I see no reason why we should guarantee owners' houses for any longer than that instead of freeing up those houses on the market for new owners.
Tax deferral is a great idea, tax relief not so much.
From my understanding part of the problem also is even landlords and businesses benefit from prop 13 and same with people that own multiple properties. Honestly, I think something like Idaho's Homeowners Exemption is better. The owner has to live in it to qualify. https://tax.idaho.gov/i-1051.cfm
Also states like Nevda have done some other interesting things like letting family farms get a Limited Allodial Title for a period in time before stopping. I just think prop 13 was not planned out very well and applies to too many entities, but the idea of not wanting to force people out their homes is certainly a problem other states worry about.