That's one of the big appeals of LVT: in theory it works incrementally. You try e.g. a 5% LVT and you should notice 5% of the effects.
Property tax isn't THAT different, and one component of it is a tax on land.
Are we seeing the LVT effects in locales with high property taxes?
That may not last long if the Texas GOP continues to emulate California housing policies by seeking to repeal property taxes; if they do that they will soon start to also imitate the California-style housing crisis.