How you got from "offer public housing" to "abolish private property" is a mental path I'd like to explore. I really mean it. Because it seems that a lot of people seem to mix up welfare state with communism and I'm trying to understand why.
Many people seem to have setup a false choice between the two. Some people, especially politicians, benefit from the false dichotomy.
I would hope that intellectually honest people can see there is large design space for the role of government. Choosing from these options — what is better and worse — depends on individual values and collective responsibilities.