They are freeing up ~10,000 houses over the next four years with this legislation. Barcelona built ~15,000 new properties between 2011 and 2020.
The math don't math. It's a drop in the bucket. The entire impact of AirBnB + all housing built in the last decade does not offset the last half decade of population growth.
Housing must be built more quickly than your population is growing to keep prices down, or you must concede that you live in a nice area where people wealthier than you wish to be and that those people are going to gentrify the area and displace locals. It's an unpleasant reality of the world.
EDIT: some good feedback in the responses. thanks! I'm being a bit dramatic by saying it's just a drop in the bucket, this action frees up more housing than was built over the same timespan, and it's possible to have effects on pricing greater than what would be inferred by the raw numbers because economics is tricky. cheers.
Will this move solve the problem? No, but what alternative are you comparing it to where it fares so poorly?
I suspect even the staunchest proponents of unregulated construction of denser housing would only claim that it mitigates the problems of housing affordability, not that it solves them. This new STR policy could be one of many pieces of the puzzle.