That's a funny point, but consider this: Land (along with regulation) is what limits the supply of housing in SF. If you transform a house to a hotel, then yes, it's true, the supply of housing has fallen. However, at the same time, the supply of hotels has risen. If the world equilibrates, then perhaps a hotel is torn down elsewhere and its land is freed up for housing. So I don't think it's necessarily the case that short-term rentals drive up the price of long-term rentals (but perhaps it is once you acknowledge that hotel rooms have higher density than AirBnB).
Also, it seems like this logic could apply to anything. Oh, you're building a Chipotle so that poor people can eat cheap food and earn money? Well that Chipotle takes up land, driving up rental prices. High rental prices means that people have less money and less of a budget for food. So the justification is: "San Francisco residents are so poor, they need the ability to become drive up prices and become even poorer!" But that seems a bit silly.
Just an aside but it's almost all regulation that limits the supply of housing in SF. There is essentially no lack of land due to our technical ability to stack things vertically.
Regulation isn't really the limit there. Regulation is the mechanism that implements the limit. The limit comes from the combined views of the citizenry about what sort of place they'd like their city to be.
Is it really the combined views of the citizenry? Or is it primarily the views of a minority of wealthy landowners who have political influence more proportional to their wealth than their numbers?
It's combined through a complicated weighting function, and we can certainly argue about that function.
But I'll note that just last year there were a pair of ballot propositions where circa 2/3rds of voters rejected raising height limits for a big new project:
I don't buy this argument at all. They were proposing to build 134 condos at $5 million each. That isn't increasing the housing supply (much), it is giving away the one-of-a-kind waterfront for some pied-à-terres for rich out of state buyers.
It's actually the other way around. Major landowners want to build more units because there's plenty of money to be made.
It's existing renters who are stopping new development. Long term renters have fantastic rates because of how rent control laws are written. And they want to keep their rent low (for themselves, new arrivals can get screwed), their streets sunny (instead of being overshadowed by high rises), and their neighborhoods not too crowded.
I live in SF and I feel something different. The regulations are consistent with versions of SF that most of its citizenry would not like (e.g. like Malibu).
This may not be important, but just to clarify my thoughts above: if we had unlimited land then things like maximum height regulations would no longer be a problem. In my mind it's the combination of limited land and regulation, not just the regulation, that raises house prices. (Not meaning to disagree with you, just to clarify.)
Also, it seems like this logic could apply to anything. Oh, you're building a Chipotle so that poor people can eat cheap food and earn money? Well that Chipotle takes up land, driving up rental prices. High rental prices means that people have less money and less of a budget for food. So the justification is: "San Francisco residents are so poor, they need the ability to become drive up prices and become even poorer!" But that seems a bit silly.