Speaking personally, the value of my house means little to me. I plan to live in this region for a long time - when my house goes up, other houses in the region go up. When my house goes down, other houses in the region go down. My house may be worth $1million, but selling it and buying another will get me the same house as when it was worth $500k.
It only matters if I decide to sell it AND move somewhere else. Which probably isn't going to happen.
I just want to make it clear that this is a choice you're afforded because of the value of your home.
You (quite literally) have a million-dollar offer on the table to move to, say, Austin, TX (or dozens of other great cities). The fact that you choose not to accept that offer does not negate the existence of the offer. The offer is always there. And this is a very real asset that you have (that, I hope it's clear, most people don't have), whether you choose to acknowledge it or not.
I'm sorry, but no. If you have a million-dollar gold statue of a pig that you're unwilling to sell, your unwillingness doesn't even enter into it. You still have the million-dollar statue and it's still worth a million dollars. It doesn't matter what rationale you provide for not selling it. It just doesn't matter. Those reasons seem important to you. But they aren't important in assessing the value of the statue.
Speaking of moving - a downside of prop 13 is that people used to upgrade / downgrade their houses. Have kids? Get a little bigger house. Retire? Downsize.
IIRC you can usually transfer your tax advantaged status to the same county if you buy a smaller place. It's a little restrictive but it still enables you to downgrade.
It only matters if I decide to sell it AND move somewhere else. Which probably isn't going to happen.