Duck Dynasty is not the show that they wanted, it is the show that got away from them.
It seems what the producers intended and what A&E envisioned with the show is much different than the show that they ended up with, but they didn't do anything about it because it was so wildly popular and so wildly profitable. But even with all the money, they have never really been comfortable with what happened.
This is what happened. The whole idea of the show was to parade these nouveau riche Christian hillbillies around so that we could laugh at them. "Look at them," we were supposed to say. "Look how backward they are! Look what they believe! Can you believe they really live this way and believe this stuff? See how they don't fit in? HAHAHA"
When the producers saw the way the show was shaping up, different than they envisioned it, they tried to change course. They tried to get the Robertson's to tone down their Christianity, but to their eternal credit they refused. They tried to add fake cussin' to the show by inserting bleeps where no cussword was uttered. At best, they wanted to make the Robertson's look like crass buffoons. At worst they wanted them to look like hypocrites.
They desperately wanted us to laugh at the Robertsons. Instead, we loved them. A&E wanted us to point fingers at them and laugh at them. But something else happened entirely. Millions upon millions of people tuned in, not to laugh at them, but to laugh with them.