On the other hand, I'd like to have a full-stack CEO as well. Not just someone who can only say "make it work", "make it faster", "make me some money".
And by full-stack CEO, you mean someone who understands all the aspects of the business and isn't a pandering, disconnected, figure-head? In a lot of companies they'd be called the operating CEO, or in more cases, the COO/president.
Am I exaggerate in terms of salary? probably... these days, who can learn every single technology (from hardware to software) under the sun?
WebServices, REST, ORM, DB, data modeling, data warehouse, virtualization, security, capacity planning, storage, performance tuning, backup and recovery, test automation (you do test your own code right? not just throwing shitty code to QA right?), build and deployment strategy.
[No, NoSQL doesn't count]