I know it's been pointed out before, and I've also had this realization, that it is completely fucking insane that New Rome has a child army defending the city full of adult veterans. I therefore propose a headcanon which only slightly fixes the situation: "we didn't think the child army was actually going to have to fight anything, holy shit"
The basis for this headcanon almost entirely lies with my #1 gripe about New Rome Worldbuilding: there is no fucking way this city of adults is actually governed by a pair of teenage generals. I genuinely, straight up, do not believe it. So instead, I've decided that New Rome and Camp Jupiter are two entities, with two systems of leadership. New Rome has their own thing, and Camp Jupiter exists alongside it, with their own internal leadership hierarchies.
It's very crucial to me that everyone understands that in this headcanon Camp Jupiter is not intended to be a child army. Yes, it's an army of children, obviously. But who the hell are they actually fighting? Other Romans? The citizens of San Fransisco? Give me a break.
Instead, Camp Jupiter is the "army" of New Rome. In the sense that, the adults of NR realized it's way easier to contain ~500 ADHD kids with varying levels of superpowers if you stick them in boot camp for the first 20-ish years of their life first, and once they're adults they can leave the legion and do college and everything. The kids of the legion do not know this. They're taking this shit deadly seriously, hence the scheming and occasional Augur murdering and social stratification amongst the cohorts. It is not good that the adults are just letting everything get a little crazy on CJ's side of things, but they also just. Don't pay attention to them most of the time. They're self-governing and being a demigod is dangerous, people die sometimes that's how it is. I did say the headcanon only slightly fixes the situation.
The praetors, by the way, are the only legionnaires who get to know that they're actually the student government to NR's school board. The pair do have some political power within the NR government, because becoming a praetor is legitimately impressive and a huge achievement for these teenagers to accomplish, and demonstrates maturity + political savviness that will serve them well later in life. Also because they do, you know, lead the child army, even if it's not one anyone expects to have to go, you know, fight people.
Being in the legion is genuinely helpful for Roman demigods and legacies! Both for the actual education on Latin, Roman history, strategy, etc, and also because it teaches the kids survival skills in a structured setting, grants them the ability to go on quests with significant legion support to gain experience (Percy was a special case), they're training in fighting and engineering skills and healing techniques etc. It's a great environment for the average plot-irrelevant Roman legionnaire. Plus then once you're an adult you can go live your normal life and look back at your time in the legion as we all do to our teenage years: "damn, it was really not that deep, but it was definitely formative!"
Of course, sometimes the legion goes fucking rogue and there's not much the adults can do, as the teenagers are actually Organized and Weaponed and they're taking all of this very seriously, so sometimes you lose all of your minors when they take off cross-country to go fight a summer camp full of Greeks, or you lose an entire Cohort to godsdamned Alaska because they were following a Praetor with a sword and a dream, which is obviously Not Good. And also sometimes, like once a century or so (or twice in two years if you're unlucky), there is an actual honest to gods for-real war and the Child Army gets to go fight in the for-real Titan War against Krios on top of a mountain/defend the city against a Giant army, which is really really bad so the adults join the fighting because the child army is not supposed to actually have to fight anything, oh shit,
But, yk, most of the time the system works out pretty well.
