I don't think anyone disagrees with the need to free up the bigger, under occupied properties for families who need them but this bedroom tax/spare room subsidy is NOT the answer.
Private lets mostly won't take people on hb, so that's not really a viable option.
I think there should be incentives to encourage people to move, pay their removal costs, give them a grant towards the cost of carpeting/decorating the new place because even if there are brand new carpets, the council will rip them out before allowing someone new to move in - and flooring etc is hideously expensive.
People on benefits generally can't afford the costs of moving, so if there was help with those expenses, I bet you'd get a lot more people downsizing. By making them pay extra when they're already on the bones of their arses will simply lead to debt, rent arrears, evictions and even more suicides.