OR maybe build more houses?
Note that Ursula Von der Leyen (president of the European Commission) recently said the EU would "tone down immigration" or something like that: but she only said it because the far-right political parties are the big winners of this SNAFU.
Also when you build more housing, you have to be careful about the solution you're offering too: in France for example absolutely horrible buildings, communist style (big concrete blocks making the individual feel like not an individual and no nature), have been built on the outskirts of Paris (the "HLM") and these depressing places became no-go zones where even cops don't dare to go anymore.
So it's not sufficient to "build gigantic buildings and put all the poor people in there": you have to find a balance with nature, a mix between social classes, etc. or you'll only reproduce the worst of the worst failure France managed to create.
This is so obviously contrary to experience and common sense I'd characterize it as delusional.
But we all know that building more highways creates more congestion because of induced demand. I suspect housing also experiences induced demand. At the same time, you could be right that if you build housing for 10 times the need, then you would reduce the demand for housing. Just like if you built highways 10 times bigger, we would not have congestion.
Can’t beat demand and supply dynamics with fairy dust.