We have that already. The California Tax Postponement Program. It stacks on top of Prop 13.

Prop 13 is just a handout, it could disappear overnight and grandma wouldn't have to pay a dime.

Land is not equally valuable so you can't look at the total land area of the USA and declare that everyone should be entitled to one tax free plot of land, land in the middle of Manhattan has a different value than land in the middle of a mountain range that's covered in 20 feet of snow half the year and is only accessible by helicopter.

Most old do not live in assisted care. And healthcare is independent of land ownership.

I didn't say "assisted care" my father lived almost his entire life on his own, but still had assistance from his children and occasionally a home healthcare worker - this is a lot harder to do if his allocated tax-free plot of land is 100 miles from family or healthcare services. Healthcare is independent of land ownership, but isn't independent of location - after one medication change, he had to go back to the doctor daily for monitoring for a couple weeks, then weekly after that for 6 months. How would he do that it it was a 4 hour round trip to the nearest healthcare facility?

Yes, people who have the property value go up around them should be kicked out of their homes. Goodbye old people and minorities who live in affordable neighborhoods that become gentrified. Kick them out on the street for failing to plan for possible future dynamics in their neighborhoods. It's the only fair thing to do.