Because the people on it are not trashy; they've been able, thus far,to be true to who they are, even if they do ramp it up a bit, and ordinary Americans relate to them.
There is an episode where one of the wives is complaining about her husband dressing out a deer in the front yard of their suburban home; apparently the school bus came up and several of the children were "traumatized" by it. My wife punched me in the arm as we watched it, because we had the same conversation about 3 years ago; sans the school bus.
I hang out and hunt with people who are exactly like the Robinson's. In fact, we have our own Uncle Si, even if he doesn't appreciate the nick-name.
Happens all the time in my suburban neighborhood.
Exactamundo.
MOREOVER, they keep it clean, say grace at mealtime, and their language is clean. UNIQUE and a moral/ethic model in today's boob-tube culture; A show that you can watch with your kids or grandkids.
Compared with the 99.9% of trash on T.V. right now. I think Duck Dynasty is fun entertainment. And I barely ever watch T.V. anymore. Love how Phil always prays and gives thanks to the LORD at the end of every episode. And they throw in a bit of a moral to the stories as well.
Bonus: There isn't a metrosexual in the bunch!;)