I'm one of 8 (1 that died before I was born, so lived with 6 siblings) so I'm not against large families at all. My entire family, all brothers, sisters, wives, husbands, grandchildren - go on vacation together every year. We love each other's company!
I'm second to the youngest, and I can tell you that while my older siblings did help both around the house and with the kids, they were not our primary caregivers. I had plenty of alone time (as did my siblings) with my parents, even when they were simultaneously handling the trials of teens in the house. Mom stayed home with us and on the weekends, Dad would take us to the zoo, or the aviary, or wherever to give her some alone time. About the only time my older siblings would babysit was when my parents would go on a "date night".
We had chores - a family with 9 people living in the house (with one bathroom

) has to divvy up the duties to make it work. But no way were my sister and I doing the laundry for the entire family at any age. When we'd get ready for vacation, my sister and I would be helping mom fold the laundry and get it packed but that was the only time I can remember getting anywhere near my brother's underwear!
I think that's the main difference in this family. I grew up in a large family and can guarantee you that had my mom not hit menopause, she'd have kept having them. But we were kids, not parents. In our family though, kids actually left the home. By the time I was going to kindergarten, my oldest brother was in college.
There is a way to raise large families without making the older siblings parent. And even without all the duties that the Duggars relegate to their kids, the children can still grow up to be close, happy, and productive.