You're confused on 2 primary accounts:
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That I am saying we can accomplish better, more equitable housing within capitalism. I'm a communist, I want socialism, and that's the first step towards communism. I am not pointing out exploitation and a solution to it as some actionable goal within capitalism, but to point to the fact that a better world is possible, and we get there through revolution.
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There has never been a society where people could not work to get better housing. Not in the USSR, with the famous soviet housing, not anywhere. Public housing does not mean all housing is the same, just that fewer people go without. Further, your wages are being taken from you, in socialism that isn't a problem, so you won't have to put in a decade of renting to get something nicer.
The joint leadership of the peasantry and the proletariat as the ruling classes of the USSR. The peasantry are symbolized with the sickle, the proletariat, the hammer. The H&S is used as a symbol for socialism, communism, Marxism-Leninism, etc.