1) Zoning laws have to change as well to actually allow development of the land being taxed toward more productive ends.
2) The land tax amount needs to be high enough that the pain of the tax effectively forces owners to improve what's on the land. A homeowner sitting on a million dollar piece of property in California taxed at ~1% is still unlikely to build an apartment complex if they like their single family home just fine and are making $200k+/year in income.
3) It could be personal bias, but a lot of LVT arguments seem to implicitly assume that more rental units is a good thing, which I don't really agree with. Personally, I'd rather see 2nd homes taxed into absolute oblivion, and I say that as someone who was a landlord for several years. Affordable housing to me means "affordable housing you can actually buy" as much as it means "affordable rent". The two do not go hand-in-hand if rental income is incentivized enough that people buy as many properties as they can get loans for (California today).