Excellent post.
It's difficult for younger kids to understand how to be relaxed, but at the same time have explosive intensity. That's part of becoming an effective pitcher, along with hitting spots, learning spins, reading batters - a LOT of stuff!! IMO, that's why many kids give up pitching after a while.
As young pitchers mature, they begin to understand how to put more energy into their pitching without "muscling it", or tensing up. Tense muscles are slow muscles - hence the "inhale - exhale" that is taught to most pitchers just after bringing the hands together.
A young girl mindlessly yelling while pitching is probably missing the point, and just hasn't grasped the principle of controlled breathing - or forceful exhaling.