I imagine it's a pretty intense job that takes up most of your life and permeates your sense of identity. Everything you said can be true and I'd still expect a CEO to be very strongly attached to their position.

CEO jobs aren't plenty like standard SWE jobs.

CEOs typically don't apply for jobs, they can't walk into a company's Career page an apply as a CEO; they are headhunted by specialized headhunter.

Yes, CEO is desperate to keep their job because if they were to let go, they won't score a much higher profile job than their current; they'd be gone to a lower rank companies bidding their luck.

I'd love to read a blog post about CEO movements. One thing they could do is raise money and start a company themselves.