Gee, how about having a parade of random people showing up at all hours of the day/night just to start? The erosion of community. Further commodification of housing so that only the rich and upper middle class can buy a house in any city?
Instead we have social mobility so that we can move anytime when better opportunities arise. That may be a good or a bad thing depending on which side you are.
Moving every time a better opportunity comes up is a privilege enjoyed by a small section of the population. The vast majority of people move rarely, and when they do move it's usually within the same locality.
Even for people who can, family (spouse, kids in school, nearby relatives, etc.), friends, and so forth tend to make moving cities a pretty significant decision at some point.
Without home ownership you are throwing away a large portion of the money you may make in your life. Even if you move frequently it still makes sense to buy so long as you’re not hitting the tip of the market.
That last point - that housing is too expensive - is not something that airbnb causes or can fix. That's a supply side problem and the solution is housing construction. It may marginally exacerbate the symptom by providing liquidity.
