The task is the throw the ball to the mitt. The distance, depending on skill level, is 60 ft 6 in. The pitch to be a strike must cross the plate between a 17 in wide distance that has a vertical dimension limit of right at the knee caps and the middle of the trunk just below the letters of the batter's jersey. The vertical dimension changes when the size of the hitter changes. Now, the ball can move in, out, up, and down depending on how it's held and thrown. Maybe the goal is the throw a strike, maybe it's not. There are so many different outcomes that could happen as the "solution" to the "problem".
Ok, now take yourself out of the task and the environment. Let's look deeper within to understand what might have to happen to achieve this necessary solution. Every pitcher has a slightly different wind-up to build up the necessary amount of energy in their body to throw the ball a certain way. Their move off the stretch may be totally different from the way they load muscles and energy in their wind-up.
Now think about how they all move. Their height is different, their weight is different, their extremities are all different sizes, their muscle mass and tone are all different, the way they activate a specific muscle group is different, their movement learning process growing up is different, the visual context of their environment is different, their emotional state is different, their drive and demeanor are different, their pitches are different. I'm leaving so much out.
A pitching coach is trying to help a pitcher figure out their mechanics, design a good approach and attack strategy, and be the necessary therapist to talk them off the ledge when things aren't going right.
The sports medicine specialist is trying to get them to move well enough so that they can stay healthy and perform to their best the entire playing season.
The strength coach is trying to build up good strength and movement so that the athlete succeeds, performs well, moves well, and stays healthy.
Each one of these individuals is trying to make the athlete better. The problem lies in the fact that there are so many differences between each pitcher they work with. It's common to use past experiences as your guide, especially when working with pitching mechanics and movement when working with pitchers. The issue here is that, as previously stated, each pitcher has a million differences between each other. Trying to make a pitcher match the way you moved is only going to work ever so often. Either the body style or movement profile should match as closely as possible. More than likely you'll improve someone only a fraction of their potential, or worse, make them worse. The equivalent to this is like making an artist paint with numbers or paint with the various materials that they're given.
The true talent of the coach or specialist is to be able to identify what materials the pitcher is working with and guiding their work and progress around their unique abilities, size, movement education, strength, and movement profiles. The ones that rest on their laurels will hit a plateau or get passed up. The ones that want to get better at working with not only pitchers, but athletes in general, must keep working, experiencing, and learning. There is a nearly unlimited amount of information to learn that will make you better, the whole thing is are you willing to put in the work to get better?
Pitchers are tricky because there are hundreds of solutions to just as many problems and each problem is in a different language. One common solution for one guy probably won't be the same for another. How many languages can you speak to help fix these problems? If you only have one language then you better learn more.
There's a lot to learn, you should never be bored.