I wonder whether this holds for people like Sundar Pichai or Satya Nadella, both of whom have a pretty strong reputation as honest and "good" people afaik.
Good is a relative term specially when CEOs of multi billion dollar companies are concerned, but you do raise a very interesting point.
I do wonder if there are truly good people as CEOs of big companies and but truly good I mean people that would be recognised as such by most people that have worked with them/for them
Interestingly, there's been proposals to try and let the market evaluate the "goodness" of a CEO. It basically involves issuing futures on the company stock which (1) only pay if the CEO is fired by date X, otherwise the futures are unwound (bought back at market price); (2) only pay if the CEO is not fired by that date, otherwise they are unwound in the same way. If the price of the type-1 future is significantly higher than the price of the type-2 kind, the market is saying that your CEO is bad and by firing them you'll end up with a better replacement.
I think the term good was used in the sense of a good person, however you choose to define it, rather than good for the company, which if I'm understanding what you are saying correctly, is what these futures are about.
In any case, I'm not sure that the market is the best judge of what a good CEO is, with its near constant fixation on the very short term.
I don't know about Pichai, but Nadella was almost certainly the product of Bill Gates having such a strong influence in the CEO selection.
I bet Bill Gates was well aware of the fact that traits such as narcissism are overrepresented at the top of companies, and so was able to make a better choice armed with that information.
The level of "badness" required probably varies based on the company's needs. Those guys might have to make less popular decisions if they were in charge of, say, Radio Shack ten years ago. Or maybe different company needs just call for different kinds of CEOs.
My read of Nadella's early changes to Microsoft was that they were pretty unpopular at first (Really? We're going to put cloud tech ahead of Windows?) and also that he made no bones about letting go of people who didn't get in line with his vision.
I do think he's doing the right thing, but I could also see an argument that he's "ruthless" when it comes to driving Microsoft in the way he sees best.
I do wonder if there are truly good people as CEOs of big companies and but truly good I mean people that would be recognised as such by most people that have worked with them/for them