As a counterexample, in socialist Yugoslavia, everyone and their dog got housing. Public companies made tons of it, towns and large part of cities were built during 60ties to 80ties. It was very easy to become the owner of a unit and most if not all became just that. It really wasn't a problem and people instead of worrying about housing thought about their hobbies, everyone on the coast bought/made boats, and people on the continent built summer houses on the coast.
Come nineties, oughts and today and the huge majority of housing units made are for tourism and speculation and are just empty most of the year. Landlords appeared too, some of those accumulating wealth from renting/Airbnb'ing their previously built summer houses, a lot came from money laundering/extraction. Housing itself has very little if any taxation so it became a wealth store and its just a big circle of socially bad incentives. Usually when there is a big political arrest it would turn our that the person had like 20 houses/flats/boutique hotels. Nothing usually comes out of it, but thats a different problem.
In the last 20 years the young people got totally screwed by lack of housing and many people emigrated unable to afford even to rent a flat and have some leftover money. Or to put it in the scale, more people emigrated than at any point in the last 150 years. People don't emigrate if they're fine with what they have. And politicians care even less because people who emigrated won't vote in the elections. And did I mention that most of them are landlords too?
My point is, a political system be it "communism" (quoting you), "socialism", "democracy" or whatever has very little with how they deal with the problem. The reality is usually much more complex than applying easy labels.