I stay in AirBNBs a couple times a year (used to do more) and I would agree it's mostly "illegal" rentals but interestingly, in the US I found more "company owns a bunch of flats" things and in the EU more "some dude owns this one flat or maybe two." (And in parts of the EU it's totally legal as long as your neighbors in the building have not managed to forbid it, which isn't always possible.)
I even have a friend who owns one flat, AirBNB's it, and rents another flat of about equal quality. In his case it's legal and a kind of interesting way to work the market; however it is ruinous to the rental market for locals.
I'm about to stay in one in Asia that very much seems to be a place someone lives about 1/3 of the time, and the rest of the time they rent it out. Apparently this is allowed there, but I'm curious what the vibe will be in a big luxury apartment building with many AirBNB listings.
I also agree that the AirBNB business model is impossible without shifting liability, but it seems like in many cases you're not so much shifting as removing it. Hotels are subject to all sorts of laws to ensure the safety of guests; these laws have developed over time and usually as the result of bad things happening; outside of maybe the US, nobody is kidding themselves that there is any meaningful liability on the part of a flat owner.