If I got a cold call from the CEO I would think they were desperate, doubt that they would be around in 6 months, and probably decide that I wanted to do business with someone more stable.
I couldn't quite articulate what was going wrong, so I just I started dialing up a bunch of people myself. "Hi, this is Sebastian... yeah, me, I run things around here... anyway, how'd you like the talk? Oh cool. Anything I could've done better? No? Nothing? Come on now, don't mess with me dude. Oh, that is interesting, thank you. Anyways, I wonder if our company can make your life better. Where you at right now? Uh-huh... and how about this particular solution? Uh-huh... yeah mate, I got something good I reckon we could do for you."
People love hearing from the high-ups in a company. And you completely lose track of real life if you're not actively spending time in the trenches. That means doing any role you yourself can do periodically, and buying tea/Japanese food for engineers and technical people whose jobs you don't understand, while really testing their patience with your dumbass, Luddite questions. And constantly reminding them that you know you're a Luddite, but you really want to understand what the hell is going on in the trenches anyways.
Call people. They love it. You won't come across as desperate unless you actually are desperate, and even then, the desperation vibe will fall off if you call even more people.
I'd even be OK with a CEO sitting in on late game sales calls/meetings, but that's a whole different issue than having a CEO make cold calls (or even having a CEO on early sales calls). It gives the impression of a one-man shop, which prospective clients will, in most cases, try to avoid.
This means he's now their go-to guy for the most trivial of issues. Besides being a PITA for the boss this also effectively neuters the account team. Not ideal.
If you're CEO and you don't understand what your engineers do, you're in trouble.
I imagine you're being facetious.
How many CEOs right now know about "canonical" now being recognized by search engines? That's the kind of thing one of your people can explain to you - "Check this out boss, we now set the canonical entry for each piece, and we control which links show up in the search engine when we put out 3-4 similar versions. I've spent the last few days updating all our archives, so you should see more consistency when current users and outside people search through the archives." And then the boss goes - "Whoa, that's awesome. Party on." Or at least that's how it should work! Airline CEOs who never do flightattending have doomed companies. Those that do have a fighting chance.