You would have to ask Mrs. Duggar that, or my Mom, who had 12 of us. My parents did ok, we are all healthy, law abiding, principled people, and wouldn’t have had it any other way.
From what I saw on the show on TLC about them, the mother takes care of the baby/youngest and the older children are each responsible for a younger child - a "buddy" they called it. Mom's "buddy" is always the baby, the rest are organized by and older one who make sure their buddy is taken care of. They didn't go into a lot of detail of how much the older has to do, but it appeared to make sure they were dressed properly, teeth/hair brushed, buckled in when in the vehicle, things of that nature.
From another practical standpoint, the mom was dead lucky that several of the older ones were girls who tend to just be better at that type of thing. I also think that chores are divied out also. One show had a feature on their new laundry facilities and one child was pointed out that it would make her life so much easier and that the new kitchen would help another.
But I also go the feeling that they all do things together a whole lot, which of course makes things easier too.
The oldest is a 19 year old boy - I wonder if he has gone off to college? Anyone know?
The older ones help with the younger ones because the parents could not physically do it. I recall my grandmother, who was one of 13, saying the girls would sit behind each other in age-descending order and braid each others' hair. Often in these big families, the older children, especially if they are females, grow up and do not have any kids because they have "been there and done that" with their siblings.
I do well to remember the birthdays of 5 little ones, 17 would be unimaginable!