There are colleges that state they are looking for leadership. It’s not a mystery, but it’s also not some sort of nebbishy statement on their part. I recommend The Chosen by Jerome Karabel for the history of admissions practices at certain colleges.
The Atlantic writer is an Oxford scholar, but according to her Linkedin profile, she’s a graduate of Exeter & Chapin. So the American setting isn’t foreign to her.
To be very direct about it, if you select for a group of people who’ve been leaders in high school, with other desirable characteristics, you have better than chance odds of ending up with alumni who are leaders in public life. So looking for natural leaders in admissions is not a method to avoid enrolling scholars.
Then again, there are many, many colleges in the United States. Many do not state as clearly as the Ivy League that they are looking for future leaders.