The idea of a “well rounded student” reflects the WASP roots of these elite institutions. The ideal “Harvard man” was a well bred WASP who didn’t appear to try too hard (which would be unseemly) and balanced academic pursuits with sports and social activities accessible to people who had connections and didn’t work for a living. That’s who you wanted running your Wall Street banks, corporations, etc. Holistic admissions is just the modern incarnation of that.
In slight defense, if you must hand the keys to the kingdom (or a substantial amount of power) to one person, you can do worse than putting them through a battery of enculturation that reduces their inclination to abuse it.
And an effective part of that litmus test could be 'already has substantial power, but is able to self-restrain their abuse of it.'