1 We had surplus housing. AirBnB would (probably) be fine from an availability perspective.

2 We have adequate housing. AirBnB would still not be good. A good portion of the available places for long term rent would be taken up by short term tenants and would drive up prices.

3 We have not enough housing. AirBnB same effects as 2, but even more so.

It seems to me that we live in situation 3. We need to build housing AND curb the excesses AirBnB. Just building more housing won't fix the problem. Just banning AirBnB won't suddenly give us an adequate housing supply.