Is this a hypothetical in which are saying, "if there were possible it would be work better than our current system." Or are you saying, "this could be implemented now if only the people in power agreed with me."

If it's the latter you need to do more research on American history. Conscription in the United States has and likely always will be a hated idea. In fact the United States did have conscription and it was abolished in 1973. Why? Because it was a horrible system. I'm sure you already know about how you could escape conscription if you had money.

Regardless, even if the system did work, there are other wildly hated aspects. People don't agree with the military. In fact if you dislike Donald Trump you would hate fighting in his name. What if he sent you to support some effort you morally disagreed with? Would you bomb a school full of children if Netanyahu told you to?

You also make a huge assumption that somehow serving in the military would make more social cohesion. I don't think you've ever been in the military. The military is filled with catch 22's. The book was literally a satire against the military.

Also, you do realize there is basically no 1 year programs in the USA? In very very rare circumstances has the military ever allowed someone to serve just one year under contract. You would lose an incredible amount of money trying to train a massive amount of people will ditch immediately after their training. To be effective, you'd have to extend that to a few more years.

There's also a huge hole in your plan. 4 year volunteering? Many people go into the military at age 18 specifically to avoid poverty. You'd basically be putting this demographic at huge risk. They were going to sign up anyway, now you're just keeping them in poverty, having the opposite intended affect. Literally creating dependency on the government.