Totally, the ability to move is definitely present. The incentive to move if one chooses is a great benefit of increasing land value, we're absolutely agreed on that front.
The problem that I'm trying to point out is the converse disincentive to stay which these policies can introduce. For instance, my family, friends, social and professional networks, and history are all within the region I currently live. If I'm priced out of this current region but am okay with moving to a different region, then this is a great situation: everyone's happy.
If, on the other hand, I want to keep living the life I've built over decades, the ability to cut-and-run with the increase in my property value is little consolation; I'll be a richer man, but I'll be forced away from my home.
I've mentioned it a few times in the thread, but just want to clarify: I'm not saying that from a policy perspective we shouldn't force these people to move in order to accommodate the needs of more people. All I'm saying is that we are giving those people who want to stay in their homes the short end of the stick with these policies.
If we look at towns and cities with super-restrictive policies (e.g. single-family zoning, locked in property tax bills, rent control, etc.), they are objectively inefficient in how they allocate land. Being a resident in one of these places, though, would lead to a pretty good and stable life.
To the residents of these locations, heavy land and property tax policies are essentially telling them "Other, richer people want to live here but it's too full, so you should find somewhere else to live". It's not hard to imagine the human aspect of the opposition (including restrictive zoning in the status quo), which conversely say "Other, richer people want to live here but it's too full, so they should find somewhere else to live.".
Again, inefficient in the aggregate, and I wouldn't argue that it's the foundation we should build policy on, but it's hard to blame someone for taking that stance.