Okay, let's thinks some of this through.

measures to remedy what they see as a “crisis” facing the all-volunteer military.

This is accurate. All branches of the military are having problems meeting their recruiting requirements, because kids in general in the US are no longer fit enough to make it into basic training in the first place. So while there are enough raw people that have the mental aptitude that are trying to get in--but just barely--so many of them are unable to meet the physical requirements that the military lacks the personnel that it needs.

He described the concept as a common “rite of passage,” one that would create a sense of “shared sacrifice” among America’s youth.

Okay, yes. This is potentially correct. However, you're also going to see a lot of resentment. So perhaps you won't see the esprit de corps that you might want.

he says leads to “unnecessary delays” and “unwarranted rejections” for some people with disabilities or other conditions who otherwise want to serve.

I was one of those people that might have been an "unwarranted rejection"; I scored quite high on the ASVAB at the time (I think 96th percentile in the mid 90s), but was disqualified because I was on Prozac. Now I would be disqualified because I'm on the autism spectrum. (I was then too, but hadn't been diagnosed.) I might have done well in the military. I might have hated it. But I never got the chance to find out.

Only 1 percent of the U.S. population serves in the armed forces, Army data shows.

Okay, see, here's a huge problem. Mandatory military service would mean expanding the military by 100x. Even if you only served 18 months or 2 years as a conscript, that's an ENORMOUS amount of money that has to be spent by the gov't feeding, housing, clothing, training, providing healthcare, and paying (since you kinda gotta pay the troops) for so goddamn many people, and that assumes that they entirely cut all post-separation benefits for anyone that is conscripted (e.g., no VA for people that become disabled, no GI Bill, etc.) The infrastructure spending alone for that, and the number of new bases that would need to be built, is staggering. Right now we spend 3.5% of our GDP on the military. Even if we went low-tech for all the soldiers that were conscripted, you could expect to see that number triple, easily. That means that you're either doing massive deficit spending, cutting everything else that taxes are spent on, or raising taxes by a lot.