How many of those leadership exercises would realistically carry over into IRL benefit after the students graduate? For that matter, how many G&T students would check out because they're focused on leadership rather than abstract problem solving?
This is probably something you couldn't do in the public system, and you would need separate schools, and arguably this is what private schools already do. Policy wise, this is equivalent to vouchers, which are immensely controversial for the same reasons gifted education is, because they stream people into opportunity - or lack thereof, when they are still just kids. You're never going to teach kids enough to overthrow you, but if you don't, what are you really educating them to become?
Even just instead of merely teaching kids how to do something, teach them how to teach it while they are learning it. Like, "To do this interesting thing, we need to solve these problems to get there. Here's how to ski, or divide large numbers, we're going to space out the repetitions so your brain will become hungry for it, and when you are showing other people, you can use this method to help them understand faster. Smooth is fast, lazy is clever, etc."
This may be different depending on where you grew up, but in my memory, the top students were too busy with sports and band to get McLeadership training as a high schooler. At least the marching band nominally had section leader positions, but the reality was more so that the adults in the room made all the decisions and section leadership roles were purely titular for purposes of helping the scholarship applications in the college search.