A society's benefit takes precedent over the desires of individuals. A society wants people living in their homes most of the time. They want the majority of housing for residents with very few, specific examples such as resort towns.
> It is the equivalent premise to saying that you should ban hotels so there are more long term residents, or known as, reduce short term housing stock to increase long term housing stock.
Again, that's not the case. Hotels are purpose built, temporary places for people to stay. AirBnB is made on the premise of converting existing long-term housing in to short-term rentals.
> You might also not hear anyone say they use cabs more because of lyft and uber but I assure you that they do. Hotels have not particularly suffered their market share because of airbnb, but airbnb is widely used in all major cities. Hostels probably took a hit, but nowhere near the usage airbnb has. Hotels ~=, Hostels -=, Airbnb ++++= => people are travelling more.
I don't have any numbers here and without doing it, I'm not going to hand wave at it anymore.