IMHO, no baseball player should be a pitcher-only at 10 years young. Lots of baseball in his future. Having said that, I have a confession to make. My son was a lot like your son.
He could throw the seams off of his fastball, and made teams based on his ability to throw the rock. But I insisted that if he was going to play, he had to be a position player as well as a pitcher.
He played for two years like that, struggling to hit or catch a fly ball. Last year as a 14 yo he had some success, and I thought he was "over the hump". He was MVP of his state tournament team and hit three triples in three games to go along with a 5 inning no-hitter. Woohoo! Dad was on top of the world. I thought he finally had gotten it.
Over the winter workouts, he was the best hitter on the team. Smashing the ball. Confident. "He's my 3 or 4 hitter, I can't decide," oozed his coach.
Then came the summer season. Strike outs, ground outs, and more strike outs. His normally high confidence on the mound when pitching began to deteriorate as his batting average plummeted. With two weeks left in his season, he is complaining of elbow pain, no doubt from all the pitches he has thrown (to his credit and in his defense, he is the team ace and always pitches against the best teams, including every championship game of every tournament until the last one because of his elbow pain).
Bottom line for me is that I wish I had gotten him together with a quality hitting coach from the start, and kept him focused on hitting.
The question is, do you want him to pitch only? To pitch only every third or fourth game, and then if he struggles maybe only playing an inning or two a week? Or do you want him to be a complete player, one that can take up a position on his pitching off-days and continue to have success?
The bad news is that position players at the higher levels have to hit, or they don't play. The good news is your son has plenty of time to work on that part of his game to where it is as much a part of his success as his strong right arm.
Good luck and have fun.