Bryan Caplan has a post about "all volunteer marriage" that starts with an interesting couple sentences about the all volunteer military: "The end of the draft is arguably the greatest policy success of libertarian economics. Libertarians still have plenty of complaints about the U.S. military. But libertarian complaints about the way the military treats its manpower have virtually ceased."
I would put it somewhat differently - the draft is one of the greatest policy successes of good economics, period. And one of the nice things about it is that it wasn't an effort restricted to libertarian economists. John Kenneth Galbraith, Kenneth Boulding, and Stuart Altman were among the liberal economists (at other times critical of libertarianism) who spoke up on the draft issue. Of course, some of the more famous paper collections and conferences were spear-headed by libertarians like Friedman and Oi, which is why you get the association. But really this is a victory for good economic analysis. People are far too pessimistic about good policymaking. Sometimes it's messy and it does take time, but it happens (and sometimes you're just not backing the right policy!).
Warner and Asch's 2001 Journal of Economic Perspectives article on the subject is probably the best known history of the role of economists in the draft.
I always seem to come back to the all-volunteer force effort for some reason, because a lot of the economists that worked on that also spoke to science and engineering labor market issues. Walter Oi, perhaps the most famous economist to work on the draft, is a labor economist who also wrote a lot about adjustment when specialized labor as a fixed factor. That's long been known to be a critical element of S&E labor market adjustment. W. Lee Hansen, another author of one of those famous anti-draft papers, wrote a couple important paper on lagged adjustment in the S&E labor market. My own opposition to supply-side policy for S&E workers has been sharpened and influenced by Kenneth Boulding's paper on "the manpower concept", a lot of which discusses his opposition to conscription. And Alan Fetcher, another economist who jumped into the draft debate early on, works for the National Research Council and has published before on the economics of science and the myth of engineer shortages.
I think the reason is simple: these are all "manpower issues" that came up in the fifties and sixties, and basically asked the question "how do we supply this important class of labor that is necessary not just to meet private, but to meet social needs?". That question applies to both the al-volunteer force and the S&E labor market, so its no wonder the same people spent some time thinking about both issues.