Harvard could dectuple the number of faculty positions, and still turn away a dozen promising qualified academics for every position it fills.

I didn't go to Harvard, but I did attend a comparable fancy lad finishing school. The notion that there's any sort of magic compared to, say, Texas A&M doesn't hold up to scrutiny. The real difference is that the reputational capital of an Ivy League school. Which means that a bunch of impressive people will bend over backwards to become associated with the school.

Which in turn makes the institution itself prestigious. Which then attracts the next-generation of impressive people. Like a social status perpetual motion machine.