At some point we'll destroy the planet and then nobody will be housed.
If your "solution" is to stop building housing, you have absolutely no solution, you just want to make people suffer.
The real solution is already happening: give women control over their bodies, economic control over their own futures, give women education and ensure that women have political power in society. That along with industrialization is how to stop population growth in its tracks.
Additionally, different types of housing have vastly different environmental impacts. Detached housing with yards is environmentally disastrous, particularly when in the woods, for people that take part in normal society. Multiunit housing takes far less materials, water, heating/cooling, and as importantly it allows loving with less transportation requirements, greatly enhancing quality of life while using less energy.
I think I've spelled out my solution to this fairy well. If yours is anything other than "make people homeless" i would love to hear it, or if you have any defense of your non-solution to ever increasing population, I'd love to hear it.
Look up induced demand.
People think our roads are too crowded, so they build even more roads. Then the roads are more clear, so people drive more. So the roads get more crowded and we build more roads...
I'm only having one child, partly because of the cost. If we burn down more of the planet to make it cheaper to have a second child, people will do that. Then people will complain it's too expensive so we need to burn down more of the planet to make it cheaper again. Then people will have three children because it's cheap...
Burn, burn, burn.
Humans have a right to housing. Saying "no more housing" but not thinking through the rest of the consequences, because you are personally reliably housed, is not a solution that a society should consider even momentarily.
Refusing to house people today because at some unspecified point after we have many many more people, is not even remotely logical, ethical, or a solution to any problem.