David Henderson gives a great talk on the role of economists in ending the draft - a subject he's written on before.
It's interesting to see this, because actually just this weekend I told my wife the story about Milton Friedman and General Westmoreland. We drove by Westmoreland St. (I have no idea if it was named for the general, but I wouldn't be surprised), and it reminded me of Friedman. She works at National Defense University, so I figured she'd appreciate it. She confirmed my understanding too that the military today (and presumably earlier for many of them) is in full agreement with Friedman on this point. With an AVF they get people who want to be there and are dedicated to the mission.
The one point she did raise - another one I agree with - is that part of what you get from the AVF is that the military draws disproportionately from lower income populations. This is both a good thing and a bad thing. It's a good thing because it's an opportunity for upward mobility, education, experience, etc. It does have a downside, of course, when the wealthy go to Congress or pick the people that do and lower income people fight the wars Congress tells them to fight. That's just something to keep in mind - it's not an argument against the AVF. Everything has costs and benefits.
The other thing I wanted to mention that I've always found interesting (and have always wanted to write up) - is that almost all the big players in the fight against the draft (from economics at least) also made important contributions to the literature on the science and engineering workforce. I think the common thread here is that in both cases they were combatting what Kenneth Boulding called the "manpower concept" (and in some of Boulding's writings, U.S. policy on the science and engineering workforce and on the draft were explicitly tied together). The manpower concept is the view that you have certain input requirements (in this case manpower) that you need to satisfy and either you supply enough manpower to achieve your goal or you have inadequate manpower. The manpower concept has no appreciation at all of the role of the price system, trade offs between goals, or marginalism.