There is a lot of empty housing in this cities, and big real state corps have fiscal advantage to take over any new building so that would not fully solve the problem in Spain at least.
people down vote me but is true, real state companies with status like socimis have 95% discount in transfer tax. For example if they buy an used house in Barcelona, they pay just 0.5% transfer tax, while everyone else have to pay 10%.
What would, then?
Taxing empty housing and forcing people to live in the place they own, rent it or sell it. Keeping houses empty is the same as blocking a street in the middle of a city. Of course, they need to build more, but that will take longer to work.