The theory is that people are over accommodated, and should move to more appropriate housing. But moving home is expensive, and these people by definition don't have much money.

I haven't seen evidence that moving these people around will make any difference to the housing shortage.

But yes, it's a good idea.

Housing benefits for cohabiting / single people is weird. Ann and Bob live in separate flats and get full benefits each. They move into a flat together, and as a couple they get less than either of them was getting singly. That system is wrong, I think.