>>53987283When it comes to military conflicts in the Pokemon world, we don't see a whole lot in canon whether it's the games or the anime. On one hand, that's because it's a kids' franchise. So if one wanted to make a more realistic fic they might deviate from canon. On the other hand, we do see some wars in canon, or at least hear about them happening in the distant past. So wars existed at some point, but it's stopped in the modern era.
I like to think about how the peaceful world we see portrayed in canon could exist, even in a more realistic Pokemon setting. Not a perfect world. Just one where war as we know it has stopped, yet international conflicts still exist. And not with the cop-out of a proxy war in a third world hellscape either.
We see no region with a modern military, but we see every region with a League. Whether the League is the vestiges of what was once a military, or a new organization founded to replace it, the League is the military now. Not a military as we understand it, but the vehicle through which conflicts are resolved. If a conflict needs to be resolved, they hold a competition between the Leagues.
Some regions still keep their League trained just in case a real war ever rears its head again. Others are complacent with the status quo.