“But they would be weeded out of actually serving by the process...We all know some misfits and some weaklings who just can’t hack it. It is better to cull them previous to their being in the actual Military getting expensive post grad, so to speak, training that they will use for a few months and probably not long enough to become good.” — we already can do this from day one of basic training up to the last day of commitment, no need to employ your proposal to meet this.
“and would get a much better sense of citizenship into the deal.” — I doubt this could happen in any significant numbers; I f you have not learned and practice the basics of American citizenship by age 18 then you are likely against what it stands.
“There would also be a much larger pool of competent and willing people who would volunteer” — you assume their experience through basic training (military indoctrination) did not sour these young people from taking a larger dose of what they just have been through; highly improbable based on my 30 plus plus of military service dealing with young troops.
“Many do not join who should for their own benefit and satisfaction because the whole concept is, at all economic and social levels, just foreign to them.” — Where to start here. I think nobody should join the military for their own benefit (who is the authority for this decision). Granted there are few exceptions who were told the military or jail then went on to be superb soldiers. Additionally, I think the great majority of young people out there know what it is like. Lots of discipline, uniformity, and following orders for the sake of being ready to go to war and defend the country; these are not as foreign, as you may think, to much of the native born American youth.
I would support, however, all males conscripted into an organization like the non-PC Boy Scouts of old. Then you would have a large pool of potential volunteers.
As interesting as your proposal is, I think there are more negatives than possible positives and the cost of failure to great. In knuckle dragging terms...the juice is not worth the squeeze.
Regards.