The government responds to the will of residents, not short-term visitors. A ban is just the residents' preference to set the number of permits or business licenses for AirBnBs to zero. A government has no obligation to accommodate AirBnB.

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?"

I find banning AirBnB a lazy form of governance, much like open container laws. "This behavior is correlated with undesirable outcomes, so it is illegal irrespective of the actual result of the behavior".

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.

Living next to tourists is unpleasant and unwanted, and is so because tourists don't really care about anything other than their short-term visit. AirBnB is not correlated with that, AirBnB is a direct facilitator of it.

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.