An overview and a personal perspective - mostly rambling, though
There are those who are willing to "oppose" the military in getting the word out to teenagers, because they feel the military will target those individuals who are economically predisposed to join. The military offers such a financially stable lifestyle that these underpriveleged youths will have no better choice than to enlist in the big green machine, and go on to be baby-eating, brown-skin killers. [/digression]
After The Fact
Once you're in, there's another part of the culture that you don't hear about so much on the outside: the drive to spend yourself into debt. Does the military do this to its soldiers, instill in them this inclination? No and yes.
The military certainly doesn't order soldiers to go out and buy that phat new tweaked out Mazda, with the Sweet Rims and the deafening bass. Many members of the chain of command and the NCO support channel counsel soldiers on major purchases and expenditures. In most (all?) Battalions, there is a Sergeant in the position of Command Finance Specialist, which requires training in budgeting and the Army Emergency Relief program. There are briefings when you first arrive on post cautioning newer soldiers against blowing their paychecks.
(Who are these soldiers who don't know that if you still have checks, you might not have money? Who are these guys that buy magazines from those girls who hit on them in the mall? Both are stories circulated at inprocessing briefs...)
But there's a bit of a culture here, too, especially amongst newer soldiers. Soldiers who already have the nice car, and befriend the new guy. There's the omnipresent signs at the dealership "E-1 and above, pre-approved, no money down." The paycheck loan places. It's worse after they get back from a deployment, and that money is burning a hole in their pocket... but even initial entry soldiers who've never held a decent job can be lured into financial irresponsibility. Yes, pay for an E-1 with less than four months isn't great, but if it's more than you've known in the past, how it compares to an E-6 doesn't matter.
If you're responsible, you can keep it under control. Live within your means, maybe put a little aside. It's a steady paycheck, as long as you don't get into trouble (although you can sometimes be at the whimsical mercy of seemingly-malicious finance personnel). That's the part that was attractive in the first place, right?
You find your personal expenditures expanding with each pay raise, and you're living within your means... except for credit. Credit isn't meant to be part of "your means", but perhaps as a supplement, something to use in an emergency or for a large purchase that you couldn't lump-sum all at once.
Personal Side
This is where I am with it: credit had become part of my means. Even $100/month, not paid off, will amount to over $1000 dollars a year... $100/month might only be one week's worth of groceries.
I'd like to feel like I have options now that I'm looking at a second reenlistment, now that I'm on orders. That credit card debt that I'm carrying makes it feel less like that...
I know another good Sergeant, a technical expert, who had wanted to get out a few years ago. He was set up... but a debt caught up to him. (A similar debt has "caught up" to me recently, but that's not the bulk of my debt... not quite half, actually.) He felt compelled to stay in due to these financial constraints. (I think our unit was better for it, but wonder if he was... he's doing well now, so it's important not to second guess it too much.)
Is this so different than leaving another career field, though? The main difference, I think, is that we have a set termination date, which doesn't (usually) happen with other jobs. Right now, I have until next November. But I face a choice now of whether I will extend my commitment, or get out at that point. This decision is pretty much final, right now... I think most business professionals aren't put in that sort of position.
On Track
Back to the initial entry soldier: what is the actual objection to recruiters letting teens know about the benefits of joining the military? Is it that they don't put emphasis on the negatives? (What employer actually emphasizes the downsides to being employed by them while recruiting? What college admits that its dorms are substandard as part of its sales pitch?)
If the military does offer that sort of financial stability, maybe the people who are getting into are doing so for the right reason? Or do they feel the recruiters are lying about that? Certainly, recruiters are trained to emphasize the selling points that are most likely to appeal to their particular target, be it a group or an individual, but what salesman is not trained in such matters?
I have seen many supervisors concerned with individual soldiers' financial problems, and I've seen almost as many soldiers who resent that sort of involvement... "Why should I have to tell my squad leader that I'm buying a car?" "What business is it of the 1st Sergeant's if I missed a payment to AAFES?" "Why should you care if I do get a payday loan?"
First, a soldier's financial irresponsibilities affect their ability to concentrate on their work, or even their ability to deploy. Soldiers who are thinking about their money troubles are less likely to concentrate on aiming center mass...
But more than that, many NCOs and officers whom I've dealt with actually care. They may not know how to show it, perhaps their tact and softness in dealing with people have been retarded by embracing their training too closely, but they care.
There are worse things that a financially impaired individual could do than get into the military.