Yes, exactly - it is the idea of "well, you can gain life experience and serve for the state". However, it is (rightfully IMO) criticized as just a cheap way of gaining labor forces. I think that German culture is generally more connected with respecting authorities, rules etc., so this attitude of " you need to return something to the community who raised you up" is still prevalent.

Since 2011 the service was not enforced anymore (but not abolished - in German it's called "ausgesetzt"), but now there is a debate again to reintroduce it in light of the war. I personally am highly skeptical of it, for the exact reasons you outlined. A year ago I have went through the process of refusing to serve in the military in a defense case. We have something here called Kriegsdienstverweigerung: you can refuse to be drafted and serve under arms if it is incompatible with your conscience. I am glad to have went through the process, but I wouldn't have done so if I were younger; in fact, I probably would've been absolutely okay with serving in the military. So instead of training people to shoot, I advocate for providing opportunities for people to learn medicine and science and stuff and leave war to professional soldiers, who aren't 18- or 19 year old enscripted boys. It is also widely known that lots of guys cheated their way out of serving (e.g. drinking a lot the evening prior, so they make a bad impression on the recruiting officer), so the system was weird anyways. So I think the current debate is between "Russia and China are a threat, we need to get ready to fight, let's pump up our military production" and "War is no option, our infrastructure is in a state of disrepair, we need to invest into schools and hospitals instead of arms, and drafting teenagers can't be the solution of the problem".