The Duggars live their lives by the Biblical model of a patriarcy. The father is the head of the household and the wife defers to her husband. Now anyone watching the show can plainly see that this couple is clearly in love with each other as if they were still in high school, so it's not as if he was leading her around and ordering her what to do. Michelle is clearly in control of her own destiny and makes decisions.
Now, again, full disclosure time, I too live in this type of marriage. For the interest of discussion, I personally have found it to be quite freeing. Most people see it as oppressive and demeaning. I find it liberating--as in, nothing is my fault! hahaha The bills didn't get paid or something was late? Not my fault, hubby is in charge! My role is to grocery shop, take care of the house, the laundry, and be the mother to our lovely daughter. Frankly on most days I'm more Peg Bundy than Joan Cleaver, but I usually pull it together and since I love to cook, things run pretty smoothly around here. But we have a sense of humour. To put in simply--my husband takes care of me by taking the role of leader. I like that. I like being loved and cherished that much that someone wants to take the burden of worry off of me and take care of me by making sure the household bills are paid, our money is wisely invested, I have money to buy our food and essentials and extras, and still trips to Europe twice a year. By the twinkle and glow in Michelle's eyes and on her cheeks I'd say she feels the same way.
As for the kids "not getting to have choices or freedom" well I don't see that. They sure get to do a lot of things. Even before TLC came along the family made regular trips to conferences and did a huge trip along the east coast. TLC just happened to come along when the Duggars were planning their trip to the west coast so it happened to get filmed and a few extras added (like Disneyland) but if you'll notice, all the kids said the Dude Ranch was their favourite part of the trip--something the Duggars planned on their own. They play family sports with other families in their worship group, the individual kids all have hobbies of their own--some of the girls do volunteer work with children. Point being---THEY DON'T FILM EVERYTHING!