Zoning laws are a way bigger restriction on housing than anything else, Airbnb is a symptom and arguably a scapegoat compared to the dampening of the demand of building new housing supply.
Maybe in America. Outside the US, that's really not the problem. It's people buying up loads of houses and apartments in town centers and pushing everyone else out. Then landlords realize they can jack up rent because they can make more money in one weekend with some foreign tourists through Airbnb than they would from a local living there.
You can build new houses. But if locals are pushed miles away from town, the town dies. A new town is formed. And if that new town gets the slightest bit of popularity on social media, Airbnb swoops in to suck the blood out of it.
It's absolutely killing communities with incomes below the US average.