Supply is artificial restricted because no one will build because either they simply can't or the value is going up too much that there is no point (which can be solved) and population is increasing.
If you built a shit load of homes there would be both more houses to rent/buy and more Airbnb options. Honestly the airbnb option in a lot of places is a problem because large hotel can't be built.
There are 827,557 residential homes in Barcelona. There are 10,101 airbnb properties. That's about 1.2%.
What you think happens if Barcelona builds another 100,000 houses/hotels?