On Twitter, Jim Holland asked an excellent question: "Should CEOs also act as chief innovators?" (Click here to read the article that inspired Jim's message.) My short answer is, start with the assumption that the answer is an unequivocal No.
If the CEO isn't able to focus on minding the business, who is? Many brilliant inventors do not have the skills to be captains of industry. And even if they had the skills, these wannabe-CEOs might inadvertantly let their personal investment in the technology distort their perspective on the business. For example, if you're not making the big money you expected, is the problem that the product lacks key features, or that you've failed to market or sell it correctly?
Obviously, it'd be silly to argue that no one could ever juggle both roles, because there's no small number of people who have succeeded at being the CEO/inventor. (Whispered aside: as a mental exercise, try not to mention Steve Jobs the next time you're in a discussion of this topic.) My argument is, your chances of success increase if you start with a different model in mind, and work your way backwards to the CEO/inventor.