Speaking as a landlord, it's even sillier than you say. My agent explicitly refuses to deal with people on housing benefits, because "it's too difficult to get the money out of the government".

I think this is bad for everyone. Poor people for obvious reasons, and everyone else because even when it works it drives up rents and by extension house prices, with the extra money going to people like me (and I left the UK).

I think the UK government should be building more council houses: https://en.wikipedia.org/wiki/Council_house