From my desk as a trial counsel (military prosecutor), your "Let's Draft Our Kids" proposal looks more like a full employment act for military attorneys than a productive use of taxpayer funds. A few of the hidden costs associated with your proposal:
1. Not everyone who starts the program will want to finish, and not everyone who signs up will want to work all that hard for the generous benefits you're offering. I doubt this will be a very efficient workforce. Between the malingerers and the shift toward a pro-welfare state attitude of the young folks who would be stuck in this program, you've also perpetuated the myth that we can continue to grow government at a time when we're over a trillion in the hole each year with no end in sight. The ironic outcome is that your future overpaid janitor is someone who started in the Defense Service Corps in 2013 and never quite got off the government dole, staying in a menial labor position with excellent benefits his whole life.
2. Criminal prosecutions: I don't know of any data on the topic, but it is my impression that there is a higher rate of criminal activity and administrative separation with the 'moral waiver' folks let in during the increase of the ground forces during the war in Iraq. These folks never would've gotten in if not for the relaxed standards in place in the mid-2000s. Proposing to put an extra million or so folks (or more, I'm not sure what the numbers look like on this) under UCMJ authority with lowered screening standards is a recipe for courts-martial as far as the eye can see. I suppose we could exempt them from the UCMJ and put them in some special status where they are treated like any other person on a federal reservation, but federal courts already have enough on-post DUI's that we send them and their caseload is already significant, so that seems like a bad idea. Plus, if you exempt them from UCMJ, you lose the ability to maintain good order and discipline, which is implicitly part of the national service rationale under which we're enacting this program.
What about drugs? Do we conduct urinalysis screenings on these folks? If not, we're not maintaining good order and discipline. This is another several thousand administrative separations a year that major posts would have to do, meaning more work for both government and defense lawyers. Plus, the other services besides the Army don't always do separations for drug use, they are more willing to take a "naked" urinalysis — no other evidence beside the positive test — to a court-martial. That's a lot of work to get rid of a janitor or gardener. I suppose we could have a lower standard of discipline with regard to drug use in the service corps, but this double standard undermines the good order and discipline we're trying to maintain, and reinforces the perception that the civilian conscripts are second-class citizens on-post.
3. Plus, do we let them marry? You refer to them as "unmarried conscripts," but what if they don't want to stay that way? If they get married, do they qualify for off-post housing with tax-exempt basic housing allowance? Do we kick them out? Is there a 14th Amendment substantive due process claim that allows them to stay in? Do we separate them the same way we do for folks who fail to maintain a valid family care plan for dependents while deployed? The JAG attorneys still have to make this happen, in an adversarial process, that takes months. That's not a lot of bang for the buck if the conscripts only sign up for 18 months to begin with.
4. Setting aside the above concerns, this would bring into the armed services a lot of young people who will require legal assistance — they're going to buy too-expensive cars, enter into questionable contracts, and generally make a bunch of legally dumb decisions. Adding, say, another 25 percent (at least, given the small percent of the general population currently serving) to the youngest and most legally needy demographic to major installations will be a nightmare for a JAG Corps already with plenty to do.
The libertarian opt-out doesn't solve these issues. We've already got a relatively small all-volunteer force that has plenty of problems along these lines, and increasing the population of folks in the military with what will certainly be lower admission standards will remake the military's purpose from winning the nation's wars to mentoring a young cohort of folks in order to instill in them discipline and a positive work ethic. We already do enough of the latter, and I fear that this proposal would impair our ability to do the former.
Which is why, if you ask the generation of officers who presided over the birth of the all-volunteer force, we got rid of the draft in the first place.