Maybe my story will help or give some perspective a bit. I played pro baseball and DI at Princeton, as a switch hitter, and I started it in high school! Most would consider that late. You and your son may be on to something..... I'll share more of my story.
I played around with switch hitting when I was around your son's age. When I got to high school, specifically between my sophomore and junior year, my coaches were very encouraging of me to switch hit. Here's what they saw and told me that contributed to their recommendation:
I was fast. Speed was one of my above average tools so they believed switch hitting could be an asset to my career, especially considering that I wanted to play college ball and pro ball.
I was a very good contact hitter and a good athlete so they thought the transition wouldn't be all that bad.
One of my assistant coaches played pro ball and was a switch hitter in his career so I was in a very supportive environment
Here's what happened:
I dove in full steam. I trained my lefty swing 2x as much as I did righty. I did dry hacks in my room/living room, took extra bp, whatever I needed to because initially, it felt awkward at times. People said my swing looked pretty good but I could feel that it was different. It did not feel as natural.
Over time, my swing got better, but not necessarily before I went through moments of struggle. In fact, I was even concerned that switch hitting junior/senior years was a bad time because if I struggled that would impact college coaches impression of me.
Well, I continued with it. It didn't matter if I struck out 3x in a game, if a righty was on the mound, I was hitting lefty. Eventually, switch hitting became one of the greatest assets of my career.
As you're considering whether to have your son switch hit, now is a great time. I think much of it is perspective. You and your son can work on something and potentially discover an asset to his game. But that's the thing... I believe at some point, it should be clear that his lefty swing does, in fact, add value to his game.
Things like above average speed, more pop from the left side, better plate discipline because of his eye-dominance, etc.
I played with guys in college who came in as freshman switch hitters and graduated as righty hitters only. From my vantage point, switch hitting just made them different but not necessarily better or brought more value. When they realized that hitting lefty was taking time away from making their righty swings better, their value increased. But again, if you and your son discover there to be some value to hitting lefty, go for it and go for it ALL IN.
Again, I just wanted to share with you my story and how things turned out from a former player's perspective who went through that transition within my game... best decision of my career!
And feel free to message me with any specific questions regarding the switch hitting process/journey.
Hope that helps some.