If they could raise rents, why haven't they already?
And if their costs go up and they can't make ends meet, they will sell the property, possibly at a loss, and the lower value will lower taxes.
But this won't happen, because the landlord's taxes won't rise. They'll almost certainly fall, as shown in the abundant data. And if for some reason the landlord's property tax does rise, it's because it's a ridiculously underused parcel in an area of really really high value, like a duplex next to 10+ story buildings. Which means it may be best to let 100-300 people use that parcel rather than ~10.
The LVT shifts tax burden away from homes and businesses and towards empty lots and parking lots.