That's a sales person.
So you are right in one direction: a good CEO often has to be a good sales person. The reverse does not apply, though.
In a stable, profitable company, you need sales to keep the business solvent. And understanding the sales pipeline is pretty essential to effectively running a business.
Where this breaks down is when the C-suite forgets that you also need a product, and you need to keep innovating on that product in ways that bring value to current and future customers. This seems to happen pretty frequently.