The best reason to continue working on the product as CEO is that you can make far better management decisions that way. Even if that 10-20% time you spend coding isn't as productive as doing sales or business development, it's essential to keep that one foot in product development so that you can prioritize correctly.
Maybe. From experience though if you don't spend that much time working on the product, you have a skewed view of the work. I think it's better to have someone who spends 90-100% of their time coding advise you on such priorities. It also shows your engineers that you know they can do the job and you trust them.
Of course, this assumes you have engineers that you know can do the job and you trust.
I'd be interested to hear of examples of successful companies (other than Posterous) where a founder is CEO and continues to develop. I would think that would be a very challenging balancing act.
