This is a really good point to ponder. I can share information that was passed on to me back in the eighties, right when weight training finally broke out of its shakles and into the mainstream of sports.
I had two good mentors on this subject: the first was John Gamble, and the second was a Dr. Dan Kulund. John Gamble was once world champion in heavyweight powerlifting, and was strength coach at University of Virginia. Last I heard, he had the same role at the Miami Dolphins. Dan Kulund is an orthopedic surgeon who was also a professor at the University. He wrote a book titled The Injured Athlete which was used as a text for the graduate program in sports medicine.
Here's the short of it. If you want to practice your sport, practice your sport. If you want to condition your body and get strong, then do weight training and other conditioning exercises. Don't try to mix the two up. What happens when you hybridize is that you unwittingly create strength imbalances in your body and actually increase your risk of injury.
In order for a body to perform any sport at maximum potential, it needs a balance of extensor vs flexor strength, and upper body vs lower body strength. Many novices to the field of kinesiology are unaware of how the WHOLE body contributes to even the most simple motions when done to maximum of potential. You only need to injure a muscle in some odd place and see how it throws everything off to appreciate this. And any CONTROLLED motion has the antagonistic muscles working in a very subtle fashion to create the precise motion necessary for an exacting outcome. Certainly pitching is an activity that requires control. One needs to learn - in a very general sense - how to get the various muscles to work together to achieve an end.
Furthermore, repeating the exact motion you do all the time with weights can....give you a repetitive motion injury. Talk about defeating the purpose of what you are trying to do! Cross training is often all about asking the body to use the same muscles, but in a different way. It gives you a break from a particular way of doing things that can cause harm past a certain point. In baseball, there's a good reason why they count pitches in a game! Why add to that stress by doing more of the same with weights?
I wish there were one really good book I could recommend now. Unfortunately most of them out in the bookstore are about bodybuilding and not about weight training. But if you buy enough of them, you can get a general picture of what you need to do. Basically you need to have an off season where you train hard with the weights. Then during the season, you lighten up a bit and use weights just to maintain the strength you gained during the off season. In general any good program is built around free weight exercises that work multiple muscle groups. The machines are brought in to finish up on certain muscles (like hamstrings) that are difficult to do any other way.
And when training for pitching, don't forget the legs, the abdominals, and the forearms/wrists.
I hope this helps. Ask more questions if you have them.