That's a good point, which gives me an even better idea. How about this one - leaders start traitless. As you reach certain milestones (perhaps similar to the BTS "quests") you obtain bonuses (and perhaps drawbacks). Thus you start with a clean slate, but as you make your choices, you become more specialized. This would have an early game that is very flexible, and an end game that is increasingly unique.
This one I could go for, all right; have posted similar notions myself. I'm inlcined to think of it as logically best assessed at the end of Ages of development, for slightly more Ages than Civ has had before. (My preference is for Ancient, Classical, Medieval, Renaissance, Industrial, Early Modern (or "dieselpunk", but that term just has not caught on enough yet) and Space Age.)
I don't think "increasingly specialised" should be the only way it can go, though. I'd like it to be possible - though hard and expensive - to make a major change of direction mid-game if that was apt, and for the traits to follow that accordingly. i'm not drawn to the notion of being stuck with one set of advantages and disadvantages in the Industrial Age because they were useful in the Classical Age.