Your weird scenario can happen with most other assessment scenarios either.

If Warren Buffett wants to increase the value of my land, he can bid up all the surrounding plots, and make bids for my land. Any sane assessment method will see that the value of my land has increased, and will increase my property tax or LVT, and I'll have to pay or face the consequences.

(In the self-assessment case, you can give people the right to refuse to sell, if they are willing to eg back-pay the difference of LVT to the higher price for the last year or so. So people can opt to pay the tax instead of moving out.

To be extra fancy, give the would-be-buyer 1% of the extra tax take to incentivise people hunting for undervalued homes and to compensate for the buyer having had to secure funding.)

I don't see that as a fair comparison. The number of people who are rich enough to buy a particular home for more than the hypothetical actual value is orders of magnitude greater than the number of people who can afford to buy up all the lots around a home at a premium and affect its property value. As a result, the perceived threat to the homeowner is substantially different. I also think you're ignoring the psychological costs of this. It doesn't actually have to happen, just the potential that it could happen would be a real fear for many people. Moving is one of the most stressful events in people's lives, much less unplanned moving. There's also empirical data showing negative outcomes for children.

If that kind of fear is a problem for people, it will just be reflected in lower market prices for land.

Someone who has more of a fear for can put up her self-declared land value. They'll pay a bit more in recurring tax, but would get a significant windfall, if their fear were to come to pass: Yes, there might be some psychological downsides to moving, but getting a extra few million dollars (or whatever) has psychological upsides, too.