1. Property tax is not land value tax, and "high property tax" does not behave at all like a quasi-land value tax even if land value is a component of the property tax.

2. No, it specifically makes sprawl very expensive relative to density, and economic decisions are largely made on a comparative basis. LVT makes it free to increase the density/productivity of your existing lot, while taking ownership of another lot (more area) introduces a huge new tax burden that you have to put to very productive use very quickly.

It's way, way cheaper to increase density than sprawl under LVT.