Genghis: This is implicit in much of the above, but I don't think anyone has said it directly: a trap that is really easy to fall into when you are eager to expand is having your cities crank out settlers when then are too small. If you knock a city with a pop of four down to two, or three down to one, it takes them a lot longer to recover pop and production than if you knock a city of, say, six down to four.
So, the reason I would avoid the production cue is that, if you aren't paying attention, it is easy to let settler-only production undermine a city's productivity until your 5-turn settler factory is a 15-turn settler factory. I know this from bitter, bitter experience.
Great user name, by the way.