The solution would be to have a special 1-2 pre-enlistment program, where would-be recruits are knocked into shape, phsyically and mentally. A significant chunk of these rejects are living on various sorts of public assistance (subsidized housing, Medicaid, and student financial aid for questionable academic and vocational programs), while making little or no progress towards becoming competent, self-sufficient adults. The money would be better spent on putting them into a military environment where physical and academic education would actually happen. Many would end up qualifying for military service, and even the ones who didn't would end up better off than they otherwise would have been. Award certificates of successful completion that would mean something on a resume. And include tattoo removal in the deal -- that will be very helpful to them when they emerge into the real world.
How about just start up PE in the High Schools and colleges again?