A random search on AirBnB for a date in December shows me about 900 "Entire Place" rentals available. I'm not saying that all those would definitely be long-term rentals in the city, but I have a hard time believing that there are about a thousand empty apartments/houses that would otherwise just be sitting empty were there not the lucrative AirBnB market.
So if AirBNB didn't exist there would be an extra 1000 units available... (I'd estimate you're realistically looking at 100 units tops)
825,000 people, assume 2.4 people per unit meaning SF will need ~340,000 housing units with a population growth rate of 0.9% each year SF will need an additional 3060 units.
So if we get rid of every AirBNB unit SF could potentially meet 1/3rd of it's additional supply for 1 year. aka. big fucking deal, what are you going to do next year?