>If you have a LVT, and try to increase the rent, your tennent wouldn’t be gaining any more value from the land that they currently are, so you still won’t be able to charge 1200.
This only holds if there's no competition between landlords - so the landlord extracts the maximum possible rent from each tenant. If I'm a tenant and living in this area is worth $1500 for me; but there are two landlords competing to have me pay them, I might end up paying $1000. If then both landlords raise their prices to pass the LVT, my rent ends up higher.
It's an empirical question and not easy to answer as to how much of the economic surplus is captured by the tenant vs landlord