So I've had the fortune and misfortune of having a CEO who was also a programmer.
To most programmers, I can imagine that the notion at first seems attractive- but very quickly questions tend to emerge..
The most obvious being- "The ability to write code doesn't mean they're going to be a good manager".
Writing code, and managing people are vastly different, let alone running whole businesses.
One very large employer who had a chairman and former CEO who was a programmer had some very self destructive behaviours, namely death marching and demonstrations of technical expertise over collaboration and listening skills. The problem is, this also encouraged others to follow suit, even "one up" each other to demonstrate they were members of the club. The only benefit, is that the CEO seemed to spend more time fighting with his own management which resulted in more softened versions of their edicts reaching the company. Fortunate, but the damage still occurred and culturally took years to undo- and didn't really start until his role changed.
Another- "As a programmer, I have a weird thing about control- I want to micro manage and change anything in my codebase- if I ran a company? jeez" this one manifested this morning for me.
I paid for services from a hosting company. Provisioning went well- all looked well. When I tried to use the services- they fell over and disappeared entirely. I waited a little while- then realised it wasn't going to resolve itself. After raising a ticket- I was informed that the CEO was in hospital having surgery, and as he was also the main programmer it was going to be 24-48 hours before the issue was resolved.
This wasn't a company that marketed themselves as a baby startup, so it was a bit of a rude shock to realise that the services you paid for, aren't coming and it all depends on one guy, who also runs the company.. sheesh!
I was educated- very early in my career by an uncle who was a HR manager- - he drummed it into my head- "if you cant be replaced, you cant be promoted"- the loophole seems to be, is being promoted doesn't seem to preclude you from being able to be indispensable- and above seems to be the end result.