A draft of enlistees (heck include some officers) will allow the USA from developing a professional or an elitest "warrior" class and keep the civilian population in touch with the needs and reality of what serving means.
First off, I strongly believe in not allowing people to enter into the military as an officer, be it by draft, ROTC, or contract. I'd much rather (and do) have superior officers that have been in my boots once upon a time and know first hand what they're sending their men to do. An officer that started as an enlistee has my full respect, while somebody that entered as an officer... well... I stand at attention for them cause I have to. That's not to say they aren't competent enough, just that they don't have the experience necessary to be a leader (case in point: Obama).
Now as far as the elitist warrior class... this can be good or bad, depending on how you look at it. From an Orwellian standpoint, an elitist warrior class can result in something like what happened with the Romans, or as described in
1984, but honestly I don't see that happening. Being part of an elite group boosts your morale and encourages soldiers to be at and stay at their best... think of the attitude that SF guys have around infantryman and Rangers.
Today in every level of government are professional politicians that have never served in the military yet are voting on veteran's benefits, military pay, military hardware, etc.
In my opinion, prior service in the military should be a requirement for a politician to be able to have a say in anything concerning the military (and to be a presidential candidate, but that's another issue).
Think of the saying "America is not at war, the military is. America is at the mall." I grew up the product of 'The Greatest Generation' every uncle, my Dad and my grandfather served in WWII because the nation was at war. During my developing years the US was flooded with vets and people who had worked for CCC and WPA. The country was prospering.
I see this more as an issue with society's way of thinking (and I do see this as an issue) rather than a reason to set up a draft. In fact, a draft could push society to have a negative view of military service, mores than its already starting to. In fact, the draft during the Vietnam era is probably what pushed society from the WWII viewpoint of war and the military to what we have today.
So in other words... I agree more people should serve. However, it needs to be a personal choice rather than a requirement. More people should WANT to serve, and that's a change that needs to happen in society rather than in gov't regulations.
I enlisted & served with both draftees and volunteers. I understand your statement it is easier to serve with someone who wants to be there, however even with an all volunteer force there are still the disgruntled personnel who go out of their way to make everyone's life miserable.
Hence the "in theory" part

My point was, I'd much rather be standing in the middle of a combat zone, trusting the guy next to me to have my back in life or death situations, when the guy standing next to me is a SOLDIER, not a teacher from Ohio that happened to be sent there. Ya get what I'm sayin?