Moving the body through space, exerting yourself in a private moment of psychological warfare will carry over to every other part of life. Training is conflict-resolution practice. Everyday we train is another chance at conflict and success, building a wall on purpose only to conquer it all on our own.
Fitness builds confidence and strength on both the outside and the inside. So, in order to be good at conflict-resolution we must practice, and our sparring partner ever at our heels is us. Entering a gym or field of fitness is to train for life; to practice and use a power within us on an external force.
However, size and strength outside of yourself will never intimidate or help you rule others, the point is to train your own mind and be strong in your own self, then others won’t even bother or shake you as much. This has nothing to do with intimidation since you are not a fighter. If you are a fighter then you would train for such an event.