Responding to LVT in this way would require an unprecedented degree of collusion among landlords. That's unlikely to be sustainable, given that a lot of rental inventory is under smaller-scale landlords who will have a much harder time holding units vacant and therefore will be more eager to cave and drop rents back down to their actual market values.

Even if such a cartel could be sustainable (say, because the vast majority of rental units are under a couple of massive property management firms instead of thousands of smallhold landlords), it'd only “work” until people get sick of it and move to other cities, thus producing more vacancies, thus (under LVT) causing those landlords to hemorrhage more money.

Put differently: every landlord already knows every other landlord wants to maximize cash flow, so if landlords were actually capable of coordinating to the degree necessary to raise rents in response to LVT without bankrupting themselves, then why are they not doing that already? Why have they not yet all gotten together and decided “we're all going to charge infinity dollars per month per square foot”?