I guess I will answer with an opinion contrary to what others have said. But each experience is different, and we all agree with that reality.
My 2017 was a two-way, but a C/RHP, which is different than your son. That is a tough combination and he knew that he would likely never be a two-way in college. But I signed him up for both at multiple showcases, which I found to be "value added" since he got to play in the showcase games as a catcher, bat and usually pitch 1-2 innings. He has a great arm, so his Pop times were always scored really high in the rankings, and he hit well enough as a catcher to be viable. His answer to me was always I will play whichever position gets me the best chance to play college baseball at a school I like.
As Senior year rolled around, he attended a P/C camp at Stanford where he had a chance to talk with their then pitching coach. He gave him some sage advice: stay a two-way player until the college coach of your school of choice tells you which you play for him. He told him not to give up playing both because it would give him more options. Interestingly, a number of the schools he was recruited by wanted him as a C, others wanted him as only a PO, and two were even saying he could do both at least as a Freshman.
He wound up as PO in college, and his coach was clear from the start that would be his future. But the coach also liked the fact that as a two-way in HS, his arm was not abused as he might have been as a PO. He assumed there was more upside in building as a PO in college when he focused on the training and regimen as a PO. So far so good.
So our experience says maybe you don't want to end that dream until a college coach tells him it is over.