Replacing cheap hotels with Airbnbs is like replacing buses with cars. Pretty soon you run out of room on the road. The problem isn't that we aren't building more roads or cars, the problem is the cars are space-inefficient. By using buses, we decrease the amount of road used per person, which eases congestion, and lowers cost (buses are much more cost-effective per person per mile than cars). So we don't need more houses, we need more (and cheaper) hotels. This would reduce demand for Airbnb, and thus reduce the number of homes bought explicitly to rent out.

But of course, who's going to pay for them and run them well? The nice thing about Airbnb is it created a competitive market, mechanisms to eliminate bad actors, customer service, price adjustments, insurance, and so on. You wouldn't get those things with a couple of hyper-efficient hotels. So it almost seems like we need the state to build the structure, and then allow people to bid on owning the rooms, and then renting them out on Airbnb. That way there could still be competition that drives all the useful features of Airbnb, but in a much more efficient form than the completely inefficient use of land that buying houses results in.