I know it would be a nightmare to balance/program, but I think that could be really, really, really fun. You could start with Greek boiler plate and cutomize it into a Crete style with their own gods...or create your own gods to be on your side. The game would have to balanced using somekind of point theory though, and that could be a real nightmare to test and play around with.
But it would make strategy incredibly fun! If your a flusher you could tailor your civ to be a brutal flusher, but you'd suffer later on...though, you could alternatively have your civ be a solid Flush defender etc . . .. The possibilities would be fun AND enduring.
For the reasons listed above though, I don't think a game designer would even suggest it...or maybe they did and the programmers/tester groaned, complained and yelped loud and long enough that it was eventually dropped.