I have to disagree with you there. Obligatory service has many merits worth mentioning:
You say "oh no, I won't be able to do and work on the things i'm interested in because I'll be learning how to kill people". Well, that's not true. Unless you sign up as infantry or some such discipline, you'll likely be learning some other skill. I for example, was a mechanic in the marines, which comes in handy every once in a while today, despite the fact that it's unrelated to my work as a computational physicist, or any of my hobbies. My time in the military turned me into a confirmed and active pacifist and anti-war agitator. It was in fact a growing experience. I think a mandatory service system, similar to Swiss system, would be very good for the U.S. 3-6 months active duty for training, and 2 weeks a summer service. Kind of like modified reserves or national guard. Pacifists can volunteer for non-military activities, like aid work, medical services, environmental recovery etc. Heinlein (and I'm not a big fan) got oner other thing right: no officer class: officers start out as enlisted men and work their way up. The swiss do that as well.
Shared service (following the swiss model) then crosses class bounds. Intelectualls have work side by side with working class uneducated joes. One of my colleagues in my studies was a fat swiss kid, who was one of those really abstract mathematicians. He wasn't interested in anything remotely practical, and he had a pretty snobby, effete attitude. Having to live a working class life for a few weeks did him an enormous amount of good, and got him out in the fresh air for a spot of exercise. This is good for national unity, and improves political dialog, since it's harder to get people to group up in us vs them groups.
Mandatory service (following the swiss model) has profound cultural influences as well. Because the military is by a vast majority comprised of citizenry who mostly have better and more rewarding things to do, the military isn't glorified. Because almost everyone is either in the military or has a kid or loved one who is in the military, it's a hell of a lot harder to get a war going. Public opposition is almost immediately against it unless they perceive a real need. It improves the culture of a military reminding it that it's all about the people. It would be a lot harder to get a bunch of students serving their 2 weeks service to shoot on another bunch of students protesting a war, for example. It also pretty much eliminates the chance of a military coup, and reduces the role of the military as a another special-interest power player.
The current military system in the United States is, frankly, obscene. It has probably the worst instance of a class structure in an already highly class aware culture. It draws the cannon fodder from the poorest population, who seldom have other options available to them. The military and the citzenry goes blithely into wars because by and large they aren't affected, and after all the solders chose to join. It has an extremely tribal in group/out group mindset, and because of this screws up the proper functioning our democracy. It's not called the military industrial complex for nothing. Further, the class nature of our culture is so screwed up, we really have people living in tiny seperate realities. My sister lives in a gated community with armed guards, ten foot walls, a private golf course and radio controlled gates for christ sake, and this is meant to be a good culture? Our political discussions sound more like people cheering for different teams playing in the superbowl than they do like informed debates about complex issues.
Shared service would mitigate all of these evils.