Its f------ GENIUS

To some degree, I think most companies hope to get a Steve Jobs as their CEO.
By that, I mean the shareholders, not the employees.

They want someone who gives is impression that: "A passionate genius is in charge here, we're special!". A celebrity essentially.
I think Tesla is a good example of why they want that.
Elon Musk has some stern detractors, but overall, he brings an air of celebrity to his company that I believe artificially increases it's share prices by a lot.

If you can get that kind of advertising value, and cultural presence just by paying some guy a 7-8 digit salary, you're actually making a pretty good profit.
It's even better if you can get rid of bad-PR just by taking off your current CEO mask and putting on a new one.
It usually doesn't work, but it's not that much money to gamble for a big corporation.

I don't think automation would work. Bots aren't good enough, and it would be way too expensive to develop a new AI from scratch every time there's a sandal.

No, what you really need is V-CEOs.
Can't find a charismatic and good-looking CEO to make factory farmed chicken cool?
Just make a CGI model of a part-chicken-part-cute-girl, and then have it voiced by a professional (and inexpensive) voice-actor.
Problem solved.

One thing sure,if this happen, there will be less sexual scandal.