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.