Well that was intentional. All the integrations with the US military didn't happen by accident.
Edit: There's no way you're going to get these AI systems and not have them integrated with the military. It's a consequence of releasing this stuff on the world.
At various times, yes. They all developed nuclear weapons, they all try to keep up with each other or at least enough to act as a credible deterrent to being attacked.
Is bombing schools and invading for no reason the purpose of army?
Some are meant to be defensive, some are meant to be for internal hierarchy reasons ... and some countries think the only purpose of the army is to invade.