It's not a zero-sum game. You can have both, but you need to build enough to have it. Regulating the use of a thing is a mark of market failure. How would you feel if the government told you that you could only use a pencil for writing because that has more social value than its use in making a model log cabin?
You're also failing to process my point: that banning short-term rentals is an ineffective lever, not that it won't have an epsilon of impact. Yes, you will increase supply by a tiny amount relative to the shortage. It will have near-zero pricing impact because the magnitude pales against the problem.
