Yeah, it's lame that they are leaching off the rest of us, but let's keep it in perspective.
Around 40,000 polygamists including children isn't that much of a drain on society compared to an estimated 12 million illegal immigrants doing the same thing.
And let's not forget one thing. It isn't illegal for them to claim welfare. By law they are simply adulterers. adultery isn't a crime. Being a "single mother" as a result of adultery also isn't a crime.
If somebody wants to make adultery a crime, I am all for it. But until then, there is almost no legal recourse for many of these polygamist families. You only hear the stories of underage marriages, but there are also those who aren't underage, but still living off welfare.
Also remember that they don't care if the state recognizes their marriage. In fact, they prefer that the state doesn't recognize it. If they weren't single mothers, they couldn't collect as much welfare. IMO, if the state would make polygamy legal, those communities would have a really hard time making ends meet, and the males would be less inclined to take additional wives or have more children.