Well, I'm old enough to be of the "kids today could use some military experience" ilk myself. I have to add that from German sources, the bit about amending the constitution appears to be further pursuant to the intention of creating a general duty beyond the military realm and substitute service for same. Which leads straight to a major problem in that it's likely to run headlong into international and European law banning forced labor, military conscription being the only exception as a possibly vital element of national security.
I've dealt with this all of my political "career". First of all, military service, or at least national security, needs to be the base of all such schemes. You cannot just oblige people to spend a year of their life on some undetermined character-building civic service with a free choice between all sorts of stuff including caring for the old and infirm, helping out in underdeveloped countries, or saving the rain forest.
What would probably work is a model we developed early in the millenium, based on a wide interpretation of homeland defense including against terrorist attacks, where you could have served in the military, police, firefighters, THW or any other first-responder organization. That was really not terribly original, since it was just giving equal emphasis to options that existed under the original system of conscription. People could actually be drafted into the Federal Border Guard long before it became today's Federal Police, and folks who enlisted as volunteers with first responder organizations for a certain length (I want to say seven years) were exempt.
Another model was similar to what France is now doing, which we termed "extended compulsory education"; kids in Germany are after all required by law to attend school until age 18 (including vocational schools in parallel to job training if going into the work market from age 15-16), so it would be easy to add a month or so where everybody is exposed to the options of military or civilian security service hands-on. You could even integrate it into the curriculum; there are already mandatory work internships in 9th grade IIRC. This was mostly aimed at making up for conscription's volunteer-generating function by internal recruiting.
There are several rather specifically German issues. One is the obsession with justice and equality, which means a compulsory service would need to apply to a sufficiently broad part of each class so not too many people are unfairly burdened or favored. That means selective service models like in Scandinavia, where you pick only the required number of the fittest, recommended early by a blue-ribbon committee under former President Richard von Weizsäcker, are right out.
Lack of Wehrgerechtigkeit is in fact mostly what led to the death of conscription; with a shrinking need for draftees, less and less people were inducted (in part by applying stricter fitness standards combined with declining fitness standards in society - but an increasing part of each class wasn't even examined anymore). Substitute service had long since become a choice rather than the exception based upon conscious objection anyway. Including women in the draft, another justice issue from the view of their male classmates, would increase the problem.
Attempts to compensate led to subsequent reductions of terms from twelve to ten to nine months, in a period where the focus went to foreign deployments for which draftees could only be used on a voluntary basis. Eventually it was felt that they were just tying up ressources in training, equipment etc. while providing no worthwhile service. Even with the change back to alliance defense, the question is how short you can make service terms to still get useful soldiers.
We discussed Swiss-type militia models with very short basic training terms and the rest of the obligation to be served in regular fiurther training, but there were economic worries. Employers don't like their staff getting off work for reserve service ever so often, and Germany is short on workforce anyway - which is a reason why professional military service is so incompetitive with the high-paying civilian sector in the first place. A lot is (post-Cold War) cultural of course, with little respect for military or even civilian first responder volunteers despite lip service. Even volunteer firefighters often find their employer pissed if they get called out too often.
This social/political issues collide with the sheer size of the German frame. We're finding it hard to recruit enough volunteers for a force suitable to our population and economic strength, but a "just" military conscription system producing useful soldiers would result in a force likely in excess of the 370,000 limit of the Two-plus-Four Treaty, and probably more expensive than we are prepared to pay for. So a cultural change is needed more than all else, and while there are some slow indications for this, it will need an extended period of a seriously perceived threat for substantial development - something our Eastern neighbors have over us, of course.