I mean, I still prefer my pitch to yours, but I wouldn't be sad with your idea either.
I don't think your pitch really combats the "people won't actually want to do the work" issue. I think in either example you'll have a lot of people who are "just here so I don't get fined," as it were.
But I think you're overstating that issue in either case. Will it have that issue, sure. But so does the military writ large. Does it impact efficiency, sure. But making an efficient, well oiled machine isn't exactly the point.
But other than that, reading your proposal again, I kinda think that the only thing that makes your proposal different from mine is the mandatory nature of the service.
The benefits you outlined are commensurate with the lower enlisted ranks in the military, so like, yeah, that's what I'm proposing I guess.
I think the benefits of forcing people to leave their bubbles justifies the forced nature of mandatory service. It a means of helping young people escape cycles of abuse, and exposing them to other cultures. It's also a great equalizer, in that it effects poor and rich alike, where your system ends up just admitting poor people who are desperate (not unlike the military as it stands.)
I'd also be open to having a program option where you can defer up to 5yrs to pursue a college degree if it's in a relevant field (civil engineering, etc) and do your mandatory service afterwards utilizing those skills. The program still pays for that college time but gets relevant use out of you at the end. This prevents people who know what they want to do from having to delay and gives them relevant job experience right out of the gate as a resume builder.
Why is this superimposed on a screenshot from Quest 64, lol?