Count me in the big family crowd (although not as big as the Duggars). There are weird families of every type. I think the Duggars did a pretty good job showing that a huge family is not as weird as people think. I think the popularity of the show is that many people wish they were part of such a large family. I don't think they were watching because they thought it was a train wreck. The Duggars were pulling off something that was not supposed to be possible nowadays.
Here in France I have the benefit that it is a traditionally Catholic country so people still remember large families. It's rare to have large families here now, but not unheard of. It's been easier here than in the US to have a large family. I think a lot of people are glad that someone is having large families, even if it's not them themselves.
There are a lot of reasons to have a large family and a lot of benefits, although it does seem that most families that are large have religious reasons. The Trumps all seem to have a lot of kids (5? each). If the family is healthy and supportive, there is always a support group. There's always someone to play with, to help you, to do things with. You are an instant party wherever you go. You can do things that teams or classes normally do. And when the kids get older, you've got a lot of healthy-minded people to spend time with. It's very nice.
We intentionally did not have the older kids help raise the younger ones, although they would babysit sometimes. They are going to college, and have lived in different places and gone to various schools. They aren't sheltered. The opposite I'd say. Socialist public high schools in France aren't really the best environments I'd say. But to each his own.
I'm glad the Duggars helped diminish some stereotypes. At least they showed that huge families aren't that bad.