If all that AirBnB did was break the law, then why did cities have to pass anti-AirBnB laws? Why couldn't they enforce the existing ones? I'm not saying that there was no breakage of any law, I'm saying that your comment implies that AirBnB's only advantage was breaking the law, and that's wrong.
The main part of AirBnB's success is that it fixes/fixed an imperfection in the market: In the places with demand, AirBnB took the low priced housing and made it available for short term lets. Yes, long term renters were the beneficiaries of the old model as it gave them a larger and thus cheaper supply of housing, but the real price is the post-AirBnB price. The old model had externalities too, they were just paid by different people like landlords and people who seek short term stays.
From a social point of view, for the long term renters, AirBnB does have an impact but the ways to combat it are similar to other phenomena that drive up rents: simply build more cheap housing. In many places in the world, there is a massive immigration wave of people from the countryside into the cities. China has recognized the problem and built housing. In the west, people are more skeptical and rather prefer the value of their homes to increase instead of people getting cheap rents. In the period after WW2, it was much different, at least in europe. Back then, we built lots of houses, for everyone, poor included.