Land value tax is one of the few taxes where the incidence is primarily on the land-owner, not the tenant. This is because it's an essential need that is of limited supply, so the price of the land rent is already set to the maximum. The landlord has to eat the cost of the tax.
He is in competition with other landlords, who can afford to charge less, he has no freedom to simply raise rent arbitrarily. When every landlord has to pay land value tax, then they all will raise their rents to accommodate it.
The Renter will pay the tax.
Landlords are running a business, they are not “eating” costs, the costs are paid for by the rent, and if the rent isn’t high enough to cover the costs, they go out of business. Every tax you inflict is simply violence against the renter. So go ahead, make a land value tax, make it even harder for people to rent.
Landlords aren't in proper competition in supply constrained cities (most of them), so they aren't actually competing that much with each other. In reality, landlords are charging as much as the tenant can afford to pay (in aggregate). This means that the tenant will not be able to pay a higher rent, even if every other landlord also raises rent, so instead they become homeless (or move back with their parents). This happens across the tenancy market, so landlords are already charging as much as they can.
