Your son sounds similar to a kid who was on my 2017's travel ball team from when he was about 12-15. The kid could fly and was a great CF and a solid hitter but not much pop. He pitched really well when needed in the weekend tourneys but did not dominate.
He got to HS in one of the top programs in SoCal with a highly successful coach who converted him to a full time pitcher despite his speed and OF skills. From what I saw, I thought switching him to a PO was a mistake since it was wasting his speed. What did I know? The kid now is a pitcher with a scholarship at a D1 program.
Like others said, keep all options open--you cannot know what his future is at 13. As he gets into HS, I would use his throwing velocity more as a gauge than how well he does when pitching. Coaches/scouts will get interested in him if his velocity is at or above most kids are throwing in his class. If the velocity is not there, he has the OF option.
My son caught in HS but it was his arm and velocity that coaches liked at the showcases, and now he is a pitcher in college. He never pitched much in HS so his arm has a lot less miles on it than if he pitched a lot previously. There is definitely a benefit to pitching training, but be sure not to overdue it.
Good luck on the adventure--it's just beginning for you and your son!