Nothing like having an army full of folks who don't want to be there. Not a good idea.
Moreover, if you had a draft, the percentage of gay people in the population would jump to 30-40%.
A draft would also have to selective and exclusionary since we have about 26 million men and women between the ages of 18-24. There is no way we could absorb such numbers in our military. Hence, most would be excluded from serving in the military. We would also have difficulty employing such numbers in national service, both in terms of numbers and costs.
Would be something like the Russian army.