I think it's a good idea, although one that I think would better suit women at either end of the age spectrum- either young women starting out in life without partners or children; or divorced/widowed older women who want community but not a partner, and whose children are self-sufficient adults.
I also think it is better suited to women who can make an informed choice to be there, and understand the rules, rather than women who are homeless or desperate and will agree to anything and deal with the consequences later.
The hardest thing to solve for me is the issue with male children. I don't know how to solve this, possibly with a guarantee of alternative accomodation for either mother and son, or son alone- but would that be allowed under allocation rules? Or perhaps a no children rule?
To the PP who said 'A work colleague of mine died a few years ago, she lived in a council house with her adult son. He was given 3 weeks to leave after she died, he was only 19.'
You say this blithely, as if it is a happy solution to the problem. I see it as an inhuman way to treat someone. It happened to someone I know when they were 18, it was awful, they had just been left orphaned but were evicted in a few weeks- all of the furniture and personal effects were sold as they had nowhere to go and needed all the money they could get for a rental deposit. They ended up sofa surfing for a while, and spent time in a homeless hostel, all whilst grieving the death of his parents. So I don't see it as the happy solution that you seem to.