I can see that. However, I am especially interested in the education of the person who is the best in the school. So much more progress is made by the top 0.1% intellectual elite.
A valid point in high school, where there are few enough very smart people that each has enough hope of being the best that it's worth competing. But if you're the top student in your high school and go to a college where you have a chance of being the top student, odds are you have gone to the wrong college rather than that you're just that awesome. If you're usually the smartest person in the room, you are in the wrong room, and all that. And if you're mainly motivated by competition, the small pond is quite tempting.
Here's an internal dialogue I just had.
Q: How do we test rationality skills?
A: We haven't come up with a comprehensive test yet.
Q: Maybe we can test some part of rationality?
A: Sure. For example, you could test resistance to akrasia by making two contestants do some simple chores every day. The one who fails first, loses.
Q: That seems like a pointless competition. If I'm feeling competitive, why would I ever skip the chores and lose?
A: Whoa, wait. If competitiveness can cure akrasia, that's pretty cool!
Now we just need to figure out how to make people more competitive in the areas they care about...