I didn't see the programme (I deliberately don't watch hate bait programmes) but I'm aware of what you are talking about. I think all the moral outrage and sniping about his looks is largely irrelevant, I also think the majority of people claiming benefits think he's a feckless cheeky sod, what can be done about him whilst still maintaining rules which are fair to the majority of families / single parents? No idea, not a lot I suspect. You certainly can't go around carting people's kids off into care though, and anyone who thinks you can or should is heading for a social apocalypse where the poor have no rights.
I think the man is the very worst kind of individual, self entitled, fecless and stupid, and i'm not thrilled my taxes pay for that, I'd rather they paid for something more worthy, but sometimes in the need to be fair to all you have to have rules flexible enough for the odd horror to take advantage of, and this is what he is, an odd horror. He's not representative of most people, and thus he's not sufficient reason to change rules which will have a detrimental effect against poor people or benefit claimants in general.