Illegal immigration is not without its problems, but the groups you described are responsible for that too. They benefit from illegal immigrants in the workforce, and then publicly rage against it. Make no mistake, the owner class does not want to curtail illegal immigration, they just want people mad at the immigrants instead of them.
I lived in USSR/ Russia, and these free housing thing didn't work out well
People had to wait for years before being assigned an apartment, which was never in the place you wanted. In the meantime, you d live with your grand- family in the same 30sq meters
This could be, maybe, improved somehow? But definitely not straightforward
To build housing requires massive amounts of labor. Labor is expensive. (Thus DIY is a thing to save money).
If there is no opportunity for some profit, no one is going to build housing, because that profit is also generated from work (by a general contractor or builder). It requires finding and buy land, conception, designing, permitting, inspecting, financing, sourcing, selecting architects, engineers, designers, and contractors, etc. And not to mention taking a big financial risk to borrow a loan or pay upfront for all the materials.
If you take away the potential to make profit from all that effort, then what you will end up with is that any housing will be built with very low effort. You will basically end up with complexes like old, spartan Soviet apartment blocks.
Edit: Basically what you're saying is "other people should work for free or very low wage, so I can enjoy cheap or free housing, because 'human rights'". Which is pretty ironic.