I agree with your point completely.
But several people are using false analogies to discredit your valid point.
For example, would you trust an unattractive plastic surgeon? That is different, because strength and conditioning is something that you can control yourself through hard work and diet. If a plastic surgeon is ugly, it isn't his "fault", and he can't fix the problem by operating on his own nose or face, right? Perhaps a better analogy would be a plastic surgeon whose wife has a large nose or small breasts, and I have never met anyone in that category.

I personally would never listen to a cardiologist or other physician who smoked or was morbidly obese.

The Majerus example makes a little bit more sense, but he is more of an exception than a rule. In professional sports, there are many examples of coaches who are out of shape and some of them weren't successful players, (i.e. Bellichek). In the pros you don't have to recruit players or even care if the players like you, the most important thing is that you know your X's and O's. But in college sports where you recruit the players, overweight coaches are much less successful. Most of the best college football coaches nowadays are energetic, fit guys who fit the Pete Carol, Harbaugh, Nick Saban, Urban, and even Bronco stereotype. People on ESPN have even talked about how successful the Texas Tech coach is because lots of recruit's moms think he is so handsome.

College coaches have to know the X's and O's of the game and be good recruiters.
As for the person who showed the USC/Seahawks trainer, he is not obese nor is he 300 pounds. He is just stout like an offensive lineman.