I just think its a bad look. I know it was all volunteer but they should have told him no. Perhaps he did serve just as well if not better than someone who wasn't an amputee - kinda like Oscar Pistorius being in the Olympics, but again the optics of it don't make sense for me.
You know what he should have done was been a recruiter. He might have been able to guilt trip some of these evaders into joining.
I've got an inkling that you have read, BILL the Galactic Hero. This is link to a preview which allows one to read the first few pages. It is in those first pages where I got my inkling that you may have seen this. Or something very similar.
The ending of the book has Bill becoming a recruiter, recreating a scene which was like where it all began.