We see these ideas echoed over and over by intensely successful people. For example, it's the same one Richard Hamming claims in his famous talk, "You and Your Research"[1]. Kayvon's talk focuses heavily on the side of academia, but the claim holds equally well in two other areas:
1. Community involvement.
As an undergrad, over-commitment to classes leaves little time to give back to the "community," for definitions of community like classmates, under-represented groups, the wider campus, etc.
For example, you can't be a great undergrad TA if you don't put close to or more work into the class than your students do. This means TA'ing should factor into your schedule like taking another class. If you're already overloaded on classes and TA'ing a class, how can you hope to contribute something valuable to your students?
2. Self-driven deeper understanding.
In all these discussions, we're starting from the assumption that the student is driven; otherwise, they wouldn't be motivated to take tons of classes in the first place.
By taking fewer classes, there's more available time for the motivated student to read an interesting paper related to the lecture that week--and read it thoroughly. There's more time to think critically about interesting, new problems, and even to discover one's own passions or calling.
As one last note; if you're a student ever in the position to take a class from Kayvon, I'd very strongly recommend it.
[1]: http://www.cs.virginia.edu/~robins/YouAndYourResearch.html