I just remember when I was school in the 60's there were a lot of games played where one person out of 30 would 'win'. Very much like professional sports. Talked to my dad whose much older. He said they didn't do that when he was a kid. I think schools don't do that shit as much because they realize that one kid has a very temporary positive experience and 29 kids have a negative one.
Seems to me where the system is fair is unimportant, first we know it's not. Second is it designed to create disparities and a negative experience for most people. From a societal point of view that probably bad. And as I like say, the needs and wants of a couple of super wealthy people shouldn't be anything society cares about.
Those are about the same odds as breaking in to the House of Lords.
Would the explanation that "while it is statistically impossible, it is strictly speaking plausible for an extremely devoted and lucky regular person to join the club" be a good enough excuse for re-introducing a landed aristocracy to American government, in your estimation?