The thing is leadership ought to be like you say. Some kind of competence that allows you to help a group of people complete some kind of task.
But let's be honest. The kids want to be student council president because it's prestigious. They grow up and then they want to be CEO because it's prestigious and well paying. They pay lip service to the idea of helping a team, but really, we know they don't care all that much. It's ass backwards, people want to be leaders because {prize} and then they think about how to get there. Sometimes we get lucky and they conclude that they need to climb the ladder by being competent (this fails a lot due to pyramid structures and politics), but often they just figure out that to seem competent, you have to shout a lot about how competent you are.
Those schools maintain their status and position by ensuring their alumni become leaders. Thus it is to their advantage.
Which brings us to the bigger picture... we live in a Darwinian word of evolve-or-die, strongest-will-survive. Thus passing on to our children the skills of leadership are part of this same desire for our children to thrive.
Money. In our society it pays more in average to be a leader.
On the why it pays more, I’d posit leaders are closer to the money source so get more negotiating power as they have more information.
Information is certainly part of it (thus why we have NDAs), but so are relationships/connections, particularly in B2B or the startup world where CEOs have to sell the company to investors.
Edit: Lol. I love the downvotes. I mean, who are you talking about? Tiger Woods? Jack Nicklaus? Or were you dragging politics into this just to make a cheap shot? If so, what’s sauce for the goose is sauce for the gander.
That’s not a dig, it just seems like a poor ROI.
The speculation that poor eyesight contributes to his functional illiteracy seems plausible.
https://thegolfnewsnet.com/golfnewsnetteam/2020/12/29/how-ma...
This article supports the numbers for Trump and adds additional information.
https://www.golfchannel.com/article/golf-central-blog/obamas...
The above article gives numbers for Obama.
https://www.businessinsider.com/trump-defends-golf-trips-fal...
This article compares them both as of the summer of their 4th year in office. Short summary, Trump played at about 2x the pace of Obama.