That's how difficulty would work if the Civ AI was more hunan-like, though. The easiest setting would be an AI that can be creative and not predictable, with virtual mental limitations in place. The toddler example was just an extreme example to illustrate the concept - imagine a 10 year old if that makes it easier to see what I'm trying to say. A 10 year old will be able to grasp basic checkers strategies, and maybe have 1 or 2 tricks up his/her sleeve, but someone in their 20s who has a decent understanding of checkers should be able to usually destroy a 10 year old. Sure, not always, and there are probably some prodigy checkers players in that age range (or maybe not? I have no idea), but most 10 year olds would be easy to beat. And maybe I haven't hung around with enough 10 year olds, but it seems if you put decent checker playing 10 year olds in a room, most of them wouldn't make blatantly stupid moves either, since at that age it seems they should be able to understand the basic rules of the game. Mind you I don't hang around many kids so maybe a 12 year old is a better example.
So it seems if we had this type of AI in the game you would get your wishes - you could play a game where you could use your exploits and strategies and usually win. And I would get my unpredictable (to a degree) opponent and not get bored with the same gameplay over and over and over.