Well, let's accept how you describe your son as a player with a pop time of 1.75 to 1.8, rockets, no lasers his throws to 2B no more than 4' off ground, hits with authority, designs his own strength, conditioning and flexibility programs and does it all at 14.
Take him to a showcase of the type you describe and what does he learn? He learns he is better than any catcher the rinky dink showcase and probably much better than any player at the other two described as small. From the way you describe him, he already knows that. What does he prove to himself or anyone that makes any difference?
Taken a few steps further, do you anticipate he will continue to progress and improve from this base going forward? What will his poptime be in 3 years. Will it still be 1.75 with others catching or surpassing him? Do you realistically think that unbelievable pop time is going to go lower? Right now you are posting that your son's pop time is equal or better than the current performance of Bryce Harper.
One question I would ask myself is whether showcasing my son now creates a risk of setting him up for failure when he is 16/17/18.
If you are one of the very few who knows with confidence your son is going to be continuing to improve over the next 3-4 years so he will continue to outperform his peers as they grow and improve, you have your answers. That will be one fine player for sure, a Bryce Harper type one would assume based on pop time alone. If that happens, you won't need to send him to a showcase. Most everyone will find him who knows baseball.
If that is not the case, and your son sees how much better he is now, and in 3 years, sees how much everyone has improved while he plateaued, what happens then?
I don't need answers. Just thought I would ask questions.