And I would bet you are wrong. There are a lot of people who are running multi-billion dollar corporations who started out with nothing and when they started out no one would even dreamed of giving them a sandwich much less the position of CEO of a major company. For instance Dave Thomas of Wendy's, Jeff Bezos of Amazon, and Steve Jobs of Apple all took their companies to the billion-dollar level.
What there are are less than 100 people in the "good ol' boys" network of board chairmen from whom these people are drawn. The best CEOs are made in house, not hired from other successful companies.
Limbaugh, with no college, literally created an industry. Would he be one of the "100 guys capable and willing to run HP"?
I actually like the people you mentioned, Dave Thomas, Jobs,and Bezos. I wouldn't hire any of them to run a hot dog stand. These were guys who built their own companies and came up from nothing. The corporate animal who steps into another company is different thing altogether. Can you imagine Jobs running Boeing? Or Dave Thomas running GE?
Boards place very large bets on CEOs. Sometimes it works out and sometimes it doesn't.