Others may chime in, but I’ve found that there is more development and mph to be found refining the delivery than in lifting weights.
Doing both is of benefit–certainly, but if I had to choose one alone, I’d say work on your delivery. Therefore, how could anyone argue that throwing is not more important than working out?
Your arm only has to overcome a 5 ounce ball. Throwing the ball a lot and training to get your pitch count up to 100 only takes 7 to 8 weeks of focused effort. I would do this first. Arm strength is not as big of a factor as some people think it is. Arm muscles are in stretch, not flex when the ball is thrown, so arm strength, per se, is really not a factor in velocity. I throw a baseball a lot harder than the majority of people who have stronger arms than I do.
I’ve seen people lift weight the entire off season and return with a 2-3 mph improvement. I can usually get someone that same improvement in just a few sessions working on their mechanical flaws.