Most of our evolutionary thinking was probably done when moving... towards food, away from predators, towards a mate, away from a mate's mate. So maybe it's a chicken and egg thing? I know I always think more clearly when out walking, and when I'm engaged in a decent, thoughtful conversation, I do find myself gesticulating.
In a rehearsed speech that kind of thing sometimes feels choreographed (think Tony Blair, not Dennis Skinner). But a bit of physical punctuation must be part of the whole body language thing we consider to be important, generally.
I also say I don't really know -- as now -- what I think about something until I've written it down. Maybe that writing/typing thing is just an extension of the gesticulation habit?