The whole scheme has been badly thought out from the beginning.
I agree that there is something wrong in the taxpayer paying housing benefit for houses that are larger than needed ... remember it's only socially rented, that housing benefit pays for, properties that are affected. Remember also that pensioners are exempt.
I also think that something need be done about the abuses of the system ... but that's another story
Why not simply give a "free" spare bedroom in the system? Surely every one must agree that the tax payer should not be paying for over-large houses that are bigger than needed., but a spare bedroom for visitors should be necessary for everyone.
So a single person, or a couple, would only have their benefit reduced in a 3 ( or more) bedroom property.
A family of three ( couple plus 1 child) would only have their benefit reduced if in a four bedroom house.
So, a spare bedroom for family interaction , and remaining outside the subsidy.
And remember, privately rented, or owned, properties, are not part of the system. I have lost count of the number of questions from people who own their houses worrying because their children have moved out and thinking that they were going to be charged the "bedroom tax"