In general, increases in the cost of land rents are an important signal that more should be built on this land; it's a bummer for current residents, but it's important that this demand is satisfied.

I believe financial instruments should help: an insurance policy taken by landowners against a rise in land value should dampen the blow. (This is somewhat related to the housing markets championed by Case/Shiller)

But in general, it would probably lead to a bigger change, that is that the property with the greatest risk (land) would likely tend to be owned by those best equipped to deal with this risk. More people would prefer to be renters (what's the advantage of landownership, anyway, other than the investment potential that the LVT would relieve?)