I think its a pretty well known, understood, and proven principal that the perception of "order" has a beneficial effect on people trying to act organizationally. If you understand how that works (and most people instinctively do), then all of the ideas about dress codes and following coaches orders are pretty easy to get your head wrapped around. Combat vets will tell you that it can mean life or death, and so they'll tuck in their shirt without questioning whether it's stupid or not, and they'll get it done because "that's what we're doing today."
You also never see the true Pros like Manning or Jeter ever discussing whether or not uniformity and dress code matters - its just second nature to them - they know they need it just like they need good equipment. And you can bet that if either of them were to find themselves on a third-round playoff hockey team, where everyone had 6-week beards, that Jeter and Manning both would have the same playoff beard as everyone else, because "that's what we're doing today"
So I think it's a little short-sighted to say something like, "tucking in your shirt doesn't logically effect performance." It damn sure does.