Would it reduce the number of tourists? Not likely, they'd just pay more to hotels (and thus have less money to spend on other things - vacation budget is usually limited, but it's distribution between various types of expense is not predetermined). Would it make Barcelona a less popular destination for non-natives? Not likely, unless it objectively becomes worse place for natives too.
NYC, Barcelona and any major city that hasn't gone the way of SF and Portland, have the same problem - a lot of people like to be there, either temporarily or permanently, but the number of accommodations, both temporary and permanent, is not infinitely scalable and runs out pretty fast, especially if the city managers aren't actively working on fixing that problem by increasing the supply - which they often don't.
Increasing the supply is hard and leads to a tangle of its own challenges. Blaming somebody else - especially somebody that doesn't even vote in the local elections - is much easier, and by the time it turns out it doesn't help - which will be some 10 years ago from now - the managers could fail upwards, retire or think about some other scapegoat to blame.
NYC, Barcelona and any major city that hasn't gone the way of SF and Portland, have the same problem - a lot of people like to be there, either temporarily or permanently, but the number of accommodations, both temporary and permanent, is not infinitely scalable and runs out pretty fast, especially if the city managers aren't actively working on fixing that problem by increasing the supply - which they often don't.
Increasing the supply is hard and leads to a tangle of its own challenges. Blaming somebody else - especially somebody that doesn't even vote in the local elections - is much easier, and by the time it turns out it doesn't help - which will be some 10 years ago from now - the managers could fail upwards, retire or think about some other scapegoat to blame.