I don't think you could have a $3500 a month LVT for an apartment that rents for $3100/mo, because the land value is not fixed.
Put another way, I think the main thing that is going to take hit as the LVT % increases is not renters or landlords, but the land value itself.
A piece of land that rents for $3100/mo may have landlords willing to pay $2000/mo for the land so they can break even after construction, overhead, etc. Absent any taxes, maybe they could pay the whole $2000/mo in interest on a loan to buy the property. As the amount of land taxes increases, the budget to make the loan payments decreases, which should reduce the property value (since the same logic should apply to all the potential purchasers).
It gets more complex once you add land speculation but I think the core logic remains the same - instead of being willing to pay $2000/mo for the property the developer might be willing to pay $2200 anticipating a speculative land return (without LVT, so higher property values), but that shouldn't change in general the market rental rate or if construction is viable, so I think the main difference with or without LVT would still be the land values.
Put another way, I think the main thing that is going to take hit as the LVT % increases is not renters or landlords, but the land value itself.
A piece of land that rents for $3100/mo may have landlords willing to pay $2000/mo for the land so they can break even after construction, overhead, etc. Absent any taxes, maybe they could pay the whole $2000/mo in interest on a loan to buy the property. As the amount of land taxes increases, the budget to make the loan payments decreases, which should reduce the property value (since the same logic should apply to all the potential purchasers).
It gets more complex once you add land speculation but I think the core logic remains the same - instead of being willing to pay $2000/mo for the property the developer might be willing to pay $2200 anticipating a speculative land return (without LVT, so higher property values), but that shouldn't change in general the market rental rate or if construction is viable, so I think the main difference with or without LVT would still be the land values.