If you DON'T use the governors and micromanage everything, how many cities do you have? If I have had an excellent expansion(first or second!), with over 15 cities, I find it quite tedious to manage all of thier moods and squares. Setting the governor to manage production and mood, I find I always have growth and max production (which is what I want anyways.) Of course, if I find myself in a 5CC by circumstance(ha!) or design I will micromanage all of my cites for maximum effect.
Honestly, I am sure it would help, but I already spend at LEAST 12 hrs on an epic game micromanaging workers, military and making plans...do I really need to spend more?
Of course, there is occasionally a 'problem child' city that needs to be dealt with usually due to corruption, and I will manage it until it is prosperous.
Just so everyone is on the same page here: I never let the governor control what I actually build. I hope no one is confused on that point, but I thought it should be said.