Many seem to already stereotype those that serve as having lower intelligence and serve because they have few other options (a crock, I know).
Actually, the accuracy of that stereotype varies greatly by geographical region. In most of the country, it is indeed "a crock"--but in some locations, it actually is quite accurate--and in those locations, the reason it is accurate is, ironically, because of the stereotype.
Where I grew up (central, rural Wisconsin), the saying about how any local kids ended up in the military was only-slightly-exaggerated to this:
"If you're smart enough, you go to college.
If you're not smart enough to go to college, then you go to tech school.
If you're not smart enough to go to tech school, then you get a job bagging groceries.
If you're not smart enough to bag groceries, then you marry your sister and take over the family farm.
If your sister is already married to your brother and they already run the family farm, THEN you join the military."
Now don't get me wrong--I now realize how inaccurate that is in most of the country. But when I was growing up, that's what the kids believed--and from my contacts who still live in that region, that's still the case. And because that's how the kids there think, none of the top, or even average, intelligence kids give any possible thought to joining the military; and therefore the only locals who enlist are the lower intelligence or juvie delinquents--which of course only perpetuates the stereotype.
And from my current contacts in the military, such as my brother-in-law (I forget what rank he is in the Marines, but he's done very well, and has had assignments in their national recruiting office), this isn't just a localized thing, but permeates a large portion of the Northern Central Plains--recruitment numbers in that part of the country for all military branches are miniscule in that part of the country when compared to the rest of the country, in large part because of this type of stereotype.