I agree the problem is the system, not the tennants. Renting to HB claimants is just too risky for sever reasons, for example ...
I rented my flat our for a couple of years. I advertised it ad "no housing benefit" as from my own experiences of receiving benefits in the past, I know how common mistakes and late payments are with our local council, and I couldn't risk losing the flat due to delays to receiving rent which I wouldn't have been able to cover. (A friend of mine waited 18 months before the council paid her HB! they list her claim 3 times! They only got it sorted when the LL issued an eviction notice.)
In the end however I did end up renting to a friend on housing benefit. Never again. When we gave our friend 2 months notice, she couldn't find another place as there was no where accepting HB. She asked the council for help and they advised her not to move out, to ignore my request to leave and to wait till I took her to court to leave, I was shocked this was their official advice, and it put us in a difficult position as friends.
I tried to resolve the situation by helping her with get flat hunt, I was trawling through several sites a day trying to find a flat for her, it was nearly impossible. Gumtree appears to be full of ads for flats for people on benefits, but you get used to seeing the same ads, the flats they show are actually generic pictures, they don't representvreal flats. They're from a website which wants you to pay to join, I never did but suspected it wouldn't have ended up with a flat, seemed dodgy to me!
After 2 months, my friend found a place by chance through another friend.
There's no way I'd rent to someone on HB again, even a friend. It's just too much of a risk IMO, which is a real shame IMO.