If someone who knows me is asked to define me, there will be none who says 'shy', then again the same person would likely tell it's been 2 years since we've spoken.
I was the CEO a startup which I had to close due to my health issues 2 years ago. Since then my social behavior has changed polarity, I have nearly stopped any real-time communication(live meeting, call, chat).
I think it was caused by the trauma from events associated with having to explain the health scenario to half-dozen visitors every day over a year(social construct in India), then going through the pain of closing the startup of 5 years(in which I was on phone every hour) and again having to explain it to everyone I know.
This might sound extreme it is, but I've never felt peace like this before. The obvious victim is my business ambitions, There's only few things you can do as an indie who communicates only via email.
Since I've been at the both end of the spectrum, I would say if you're an introvert CEO then you need to have someone else i.e. 'a people person' to do all the extrovert things required for a business. I believe many successful business are run like this because the CEO can put their energy where it matters the most i.e. making money.