I've read a few of these crossovers and the central tension always seems to be magical thinking clashing with a rigid, non-magical command structure. How does a wizard who's used to solving problems with a wand and a clever plan adapt to a world where the only acceptable solutions are physical drills, weapon maintenance, and following orders without question? The fics that work for me explore that disintegration of his identity. He can't just 'Reparo' a broken Humvee or 'Obliviate' a superior officer. The struggle isn't about power, but about learning a completely different kind of discipline, one that deliberately ignores the tools that have defined him since he was eleven. His survival instincts, honed against Voldemort, might even be a liability; in the Marines, initiative has to be channeled through a very specific chain of command.
Another huge hurdle is the psychological distance from his old life. No owls, no Floo calls, no magical support network. He's truly alone, often under a new identity, which forces a kind of introspection he never had time for at Hogwarts. The best stories use the grueling physicality of boot camp as a backdrop for this internal breakdown and rebuilding. By the end, the question becomes whether the person who emerges is still Harry Potter at all, or something new forged in a crucible he chose for himself, far from the wizarding world that both saved and tormented him.