That does not solve the other large problem; most residents do not want to live in a hotel district with other tourists, and especially not as hallway or floor mates. And residents do not want new hotel builds or conversions competing with apartments. With traditional hotels this is solved with permits and zoning, but AirBnB is usable on pretty much all residential units.
Saying moving is an option trivializes how difficult moving can be, and is about as helpful as saying, "If you don't like the current president, why don't you just move to another country?"
The other argument I see is that it prices out locals. Sure, allowing someone to own a 6-unit building and rent it out as a de-facto hotel will increase housing prices. But allowing locals to rent out their apartment while they're traveling has the opposite effect - it makes property more affordable by increasing utilization.
Allowing people to rent out their apartment doesn't make property more affordable, it allows people to bid up rents with AirBnB income and it prices out people on the margins unable or unwilling to rent out their own home.