None of the 7 people I know who joined the armed forces meet your stereotype. One was a football player in high school but that's as close as it gets.
My very close friend joined the Marines. This is the guy who refused to play a game when we were in high school because it involved cracking an egg on my forehead. I told him it was ok, but he just couldn't bring himself to do that to a girl.
He is one of the most gentle, thoughtful and protective people I have ever met. He joined the Marines for the educational opportunities it provides, the ability to play with technology he would never have access to otherwise, and because he has a deep-seated motivation to serve.
He's far from the low-potential person you describe. He was a math prodigy as a child, and after serving three tours in Iraq he entered the aviation electronics industry. He married and supports his wife in her pursuit of global social justice. causes.
Another friend of mine, the high school football player, joined the Marines and was one of the front line folks in Fallujah, and he chose to re-up when his first enlistment was over. He is no intellectual slouch. Now that he's out he's getting his PhD from Columbia in organizational psychology, with plans to join the venture capital world.
A female friend opted to join the Navy. She was a 4.0 student, cheerful and friendly and laid back as they come, and she is a lifer, LOVES her military career.
You have some bad biases, you really should see to that.