> Housing costs are not up because of Airbnb

I think they are partially. In London, rents have decreased 25%-50% since COVID. Part of that will be reduced demand. But I have also seen a lot of rooms advertised for long-term rental that were previously Airbnbs.

We could certainly ameliorate this by building more houses. But here in the UK we're a lot more limited by available land space than you are in the US. And while there is limited supply it makes sense to prioritise making primary dwellings affordable over profit making for landlords.