Why would they as long as they find a renter? The market always charges the marginal cost.
1) Cost of land per year (which won't change as you'd be paying $10k a year tax rather than $10k a year in interest on the loan taken to buy the land)
2) Cost of building per year (which won't change)
Not to mention that many real estate investors don't use loans, and that the banks giving out loans understand the lack of equity being built and demand higher interest given the inherently lower collateral (greater risk).
Currently the purchase price of the property includes a good deal of future land rent, you just pay the current owner.
If you spend $50k on some land and pay 5% a year you're paying $2500 a year in rent, but you're paying that to the existing owner.
Under an LVT you'd be paying $2500 in rent, but the land itself would cost basically nothing.
Whether it's a loan, or the opportunity cost from not putting the capital elsewhere, doesn't matter.
Land speculators profit from land values increasing, and they do nothing other than gamble. They don't increase the value of their own land, that's what their neighbours do. LVT removes that speculation, and indeed risk. If the area goes downhill (say in Detroit), your taxes lower
The downside of this is if you have taxes funding the government, you end up in a death spiral. That's what the UK has with council tax (which is very regressive, a 10m house in one area can pay less than a 100k flat in another, and even in the same area would only pay about 3 times the price), and I believe it's the case in the US.
That's why I'd rather see a citizens dividend than just cutting taxes.