>Institute an LVT and those competing landlords may become cashflow negative, forcing some of those units off the rental market entirely (typically to sales to owner-occupants, sometimes to landlords with better financing or lower overheads, sometimes to short-term rentals or other higher cashflow uses).

Well, LVT is always meant to be a replacement for conventional property taxes so depending on how it is implemented it can be roughly the same as the previous property tax or it could be significantly lower because only the land is taxed and not the whole property.