This seems like a system that can only work in a fully urbanized country.
Otherwise, a nonexhaustive list of problems it seems guaranteed to cause:
- Push those currently in rural poverty over the edge into homelessness. Their homes will stand vacant and fall to ruin, leaving large swaths of land dotted with the wreckage of houses, trailers, and even whole villages. Some of it will be highly toxic. Many of the people will die, because the area they're in has precious few services for them, and they're too far from cities, with no means of getting there (because their cars have already been repossessed).
- Destroy green spaces. Parks, wildlife refuges, and even fallow fields are vital for the health of our ecosystems, the conversion of CO2 into oxygen, erosion prevention, temperature mitigation, and even mental health. And that's assuming there are explicit exemptions for farmers.
- Wreck entertainment businesses like theme parks, water parks, etc.
I'm deeply skeptical that a land-value-tax system can be calibrated so that it's sufficient incentive for developers to build up within a city, while not also causing these devastating knock-on effects in rural and suburban areas. And regardless of one's feelings about urban vs suburban vs rural living, I think we can probably all agree we don't actually want to make the entire surface of our planet into skyscrapers.