Take a city/place.
Calculate how many people visited it before AirBNB.
Let's say 1,000,000 stays per year, with an average expense of US$ 180 each, including night at US$ 120 at the hotel and some drinks/meals/souvenirs/whatever another 60 US$ .
The city/place (globally) has had an "income" of 180,000,000.
How many more people visited the city place after AirBNB became popular?
Let's say 1,200,000, i.e. a 20% increase, and let's say that not only these 200,000 more stays are at AirBNB's (i.e. people that wouldn't have come if AirBNB's were not available), but that also a part of the same people that would have take a hotel room passed to AirBNB's, let's say 100,000.
Now, the hotels will have lowered their prices because of the competition, and - more generally - an AirBNB user (with of course the usual exceptions) is probably less prone to spend money.
So we have 900,000 nights at a "discounted" price of (say) 110 US$ i.e. 99,000,000 plus 900,000 at the same US$ 60 54,000,000 and some 300,000 AirBNB's at (say) 60 US$ , i.e. 18,000,000, plus 300,000 at a lower US$ 40, that is 12,000,000.
From the 18,000,000 you have to subtract the commission AirBNB takes, which should be on average (both guest and host commission) around 15% that "goes elsewhere", i.e. 2,700,000.
The city/place received (globally) 99+54+18+12-2.7=180,3 millions, i.e. roughly the same as before, while having (still globally), the increases of traffic, garbage, noise, etc. due to the 200,000 more visits.
In the meantime, hotels and other trades had a roughly 10% decrease of income, apartments/flats were not available to local population at "fair" long term rent prices, the increased income from the rentals of the AirBNB's and connected services very likely went in a lower tax bracket.
I would say that it is not a particularly good deal for the city and for the locals.