You keep asking variations of the same question…I get it, you are trying to gain information and that is great. Most guys your age don’t care enough to try and gain information.
A quick question…in what sport would being weak be better than being strong? None of course.
To put it another way, the average MLB pitcher checks in at about 210-220 lbs. With rare exception how many of these guys look fat? Hardly any. Translation is they are strong as hell.
Here is a few quotes from a Mark Rippetoe (if you don’t know who he is, look him up) article from T Nation:
“Not every force application involves maximum force production, but the stronger you are, the better you’re able to produce force in situations where your strength must be used repeatedly, quickly, slowly, irregularly, or differently, in positions of balance or imbalance, while fresh or fatigued, recovered or sore, distracted or focused, for a few seconds or a few hours or days…”
"But the most efficient way to get strong is to lift heavy weights in a bilaterally symmetrical position, which allows the most weight to be lifted and therefore the most strength to be built.
This is why baseball players should all be squatting, pressing, and deadlifting correctly with very heavy weights: it makes you strong – like steroids, only much, much better – and doesn’t involve a Senate hearing."
So, yes, strength matters.
I think many young players get confused because they see the Throwers 10 exercises for the cuff and think all upper body lifting should be light. The cuff exercises are very important and need to stay below 5 lbs. Bands are great and again are not heavy weights. But, other upper body work…Zottman Curls, Tricpes, Rows, Pulls Ups (body weight and weighted), Pushups, Dumb bell Bench press ect should be done to gain strength.
Foam rolling, stretching and mobility work are important as well of course. If you recover and lift correctly you should not become “muscle bound”. Something like executing a proper dead lift or squat with heavy weight is doing more to work the core of the body than crunches for example. Lifting weights has carry over to many areas of performance.
I have seen guys who throw hard (88 +) who are relatively thin, I have seen hard throwers with quirky mechanics I have never seen one or known one that was functionally weak.
Make sure technique is great. Be smart with your lifting. It takes time to build up to big numbers. Recover well.