You’d just swap profit for influence instead. Look at the USSR, they had issues feeding their population, yet the people in power largely got whatever they wanted.
So the profit motive certainly has some benefits. It also has downsides, such as unequal Income distribution. But then, existing examples of communism/socialism also have similar problems.
So I think the discussion about economic system misses the mark. We can regulate capitalism to provide many of the benefits we want, so the discussion should be on what we actually want and what changes we need to make to get there. For housing, we could solve the problems we see in a number of ways, each with downsides, such as:
subsidize renting
increase property taxes to reduce vacancy
add a vacancy tax - probably harder to enforce
build more public housing - I haven’t been impressed with section 8 housing, so I’m not bullish on this one
rent controls - seems to backfire more than help because it removes the profit motive to improve rentals
And so on. Switching the economic model comes with huge costs and I’m not convinced it’s actually better than fixing what we have.