Weeks were originally based around market day: you'd work your fields for 6 days then go into town on the 7th to trade, socialise, etc. Basing weeks around a day of rest was a Jewish innovation.
There are examples of places using 8 or 10 day weeks (e.g. the Roman Empire, revolutionary France, the USSR) but everyone keeps returning to a 7 day week.
I think we'll just have to wait and see how it goes. I don't see many people becoming homeless just to get a free house, and there are ways to prevent housing projects turning into ghettos. I'd be more concerned about whether they have knowledge/skills/motivation to live in a home. I suppose case workers will help with that.
There are examples of places using 8 or 10 day weeks (e.g. the Roman Empire, revolutionary France, the USSR) but everyone keeps returning to a 7 day week.