My guess would be with the way TPTB have attempted to navigate US society towards a softer, more egalitarian "progressive" culture and make traditionally aggressive masculinity a negative thing, "They" were afraid of an already armed population being not only more effective with their weapons, but also have the combat tactics training to use those weapons effectively. Mandatory military service is fine for a country where the owning of weapons is strictly limited or banned outright, but for a country like the US where there are enough privately owned firearms to arm every man, woman, and child? I'm sure that TPTB in their infinite distrust of the average citizen were paranoid that it would be a recipe for revolution if implemented.
And then there is the -*ahem*..."multicultural" aspect of America. Mandatory military service is a great way to train "certain demographics" who are more prone to violence and crime to become more effective in those acts. Instead of your stereotypical Basketball-American holden dey GLOCK fo-tay wit da switch sideways and above their head, mag dumping in the rough general direction of the other young scholar they are trying to zero, you would instead have them becoming far more deadly because they would now know proper firearms handling and marksmanship, and that those funny little bumps with dots sticking up from the slide are actually used for aiming the weapon so the bullets will actually hit what you want them to.
If we were ever to become a high trust society full of civilized men once again then Mandatory Service might make sense. Until then, having a professional volunteer military force with the option of the draft should things become truly dire makes more sense for the kind of culture we currently have.
