I think the Duggars make it because of the show. In the first special, they were living in a rented home that was no where near enough for their needs. After a few specials, they built their nice new home (with a little extra decorating help from the network). I'd imagine that the show is their main source of profit, and has been for many years now.
Outside of that, I disagree with many of their beliefs, but they can believe whatever they want. I'm sure they'd disagree with many of mine as well. I think it's medically irresponsible for them to try and have any more children after Mrs. Duggar's body failed her during her last pregnancy, but no one can stop them from doing it.
I've also assumed the reason they're encouraging the girls to be nurses is so that they don't have to rely so much on medical facilities in the future. The Duggar grandchild was born at home with a midwife, and I'd imagine there's going to be a lot more of that in the future. No need to go outside of the family if there are midwives and nurses living right in the home. I would imagine that some of the girls are encouraged to get teaching degrees for the same reasons. Open up their very own one room school house, and just teach the family members.