Well, its a social signal isn't it.
Take a job interview at an investment bank. It is incredibly important, if you want to get the job, that you simultaneously deny being primarily motivated by money, power, and status, while sending the social signal that you are in fact primarily motivated by money, power and status. If you weren't, you're probably making a mistake applying for a job at an investment bank (although I believe the joke about someone writing on their resume/cv/cover letter about their "lifelong passion for taxation/equities/super funds" did the rounds a few years ago).
So you get your extra-curriculars/interests/academic quals to do the dance about how well a rounded person you are, but simultaneously you must wear the right clothes, drop the right names, read the right things, follow the right topics, and say the right words to strongly signal that your main motivators are in fact money, power and status and that you accept that. And if, god forbid, you're ever asked the question outright, you must find a way to explicitly deny it, while sending the subtle message that is completely the opposite.
Similarly, what are colleges selling/interviewing for? Well it sure as hell isn't skills or merit, because most rich people didn't use skills or merit they got from university to get rich, and many of them could be gotten at a similar standard for a far cheaper price.
God no.
Connections. Power. Links. And the hunger for doing what is required for more of it.
And that's what "leadership" signals. That you care about it. That you want it. That you'll be surrounded by others who think and want the same.
That's what elite universities are selling.
As for the rest, well, that's probably just regular human imitation/cargo-cult mentality. It seems almost second nature for humans to mindlessly try to imitate those they find socially powerful.