nothing is stopping people from building enough housing save the desire to keep prices artificially high
I don't know where you're located. I live in a big European city. The space here is limited. The new housing is mostly being built outside of the city really, and it will take years for it to get the proper treatment (like buses, trams, metro line). The immigrants are directly competing with me for the in-city apartments. This could be different if you're located in, IDK, Iceland, where the space is not really a problem, or in USA where you don't have public services.
our shit wouldn’t be as cheap
Our cheap shit is imported from cheap countries though?
Given more demand yet they could have built more but little enough to again maximize gain
In 10 to 20 years. But the problem of competing for limited resources is now. Seeing a problem here?