I was half-joking, but w/e.
No, really, this isn't a show about soldiers - it's a show about a world where the war ended and soldiers are not needed anymore, and where the only important role they play now is to be keepers of tradition - at least that's what I got from it so far.
Oh, of course there is a military theme but it's obviously not the point of the show. It's not a show about, war, fighting or killing, so saying that moeblob characters don't fit because of it is just plain silly. And anyways, if you think cute characters somehow detract from serious themes, what are you doing watching anime?
Now, about the "joining the military to learn music" - it makes just enough sense to me, considering the setting, and what we know about Kanata. If the war was long-lasting, then the soldiers and military were probably glorified. For the kids they were the heroes, and now that the war is over(or just de-escalated to the point seen in the show) having the desire to join the military is understandable. And playing music? Well, if that's what she can be useful at, then why not? Makes as much sense as someone with an affinity for engineering joining the military to become a mechanic.
Also
Rio quite obviously equals Mio with a different hair color
Because she has the same hairstyle? Riiight.