You won't see a land value tax for the same reason there are constraints on housing supply: because existing homeowners are essentially single-issue voters when it comes to do with anything about housing. Aesthetically progressive people turn into raging fascists the second you propose building slightly higher density housing near a train station that they're nowhere near.

In my ideal world I would:

1. Massively hike property taxes on non-income generating housing;

2. Make anyone owning housing subject to state, local and federal taxes on their worldwide income;

3. Get rid of preferential property tax rates and caps on property tax increases (eg Prop 13 in California). If you want to not force old people to sell immediately, defer their property taxes until death. This is exactly what Texas does;

4. Build for transit; and

5. Have the government be a massive supplier of social housing.