You forget that over 75% of age eligible people are not eligible due to other factors http://www.missionreadiness.org/2009/ready_willing/
The biggest factor is physical, there are also major issues with education (not meeting standards), and criminality. The physical factor isn't even just the weight. As the report states, even if the overweight candidates were to loose the weight, there are still underlying physical factors that would leave them ineligible for enlistment.
The report I linked to is worth the read. Even if you are not interested in enlistment, it provides a view of America as seen by the bottom 50%.
I am one of the many people in America who planned to do just what you suggest, I planned to join the military to pay for college; however, it turned out that I have one leg 1.5cm shorter than to other. This left me ineligible for enlistment.
I still worked hard and eventually finished my MBA; however, I finished it in my 40s’. As such, I didn’t have it in my youth and I didn’t make the contacts that are needed along the way. As a result, it really is, essentially, worthless.
On a national basis, not only has the nation lost my productive ability (chosen to operate inside of the production possibilities curve); but, working as a security guard and dishwasher, I am paying on the deferred payment program. This means that the nation is not even getting paid back. This story is repeated by people all over America.
If not for a very minor medical issue my life, and my level of productiveness to society, would have been much different. But, no, enlistment is not the ‘simple’ solution to college woes for Americas poor; not until the enlistment standards are matched to the actual MOS.