Usually players bat in a particular batting position for a reason. There are all sorts of problems associated with shuffling the batting order.
Your average opener might do fine against the new ball, but struggle against spin early in their innings, thus batting down the order could be tricky. Similarly, a strong middle order batsman might get out early to the new ball, especially on a lively pitch, and then your middle order is exposed. And really, players perform best when given a consistent role. A player who doesn't know where he will be batting will find it more difficult to prepare and perform consistently.
This mostly relates to test cricket though. If you're talking about ODIs, there's more room for this sort of thing and some teams do it. Australia used to shuffle Bevan around the order a fair bit, and South Africa seem to do the same thing with a few of their players, like Kallis and Boucher. India with Dhoni a bit as well. Even in ODIs though, there are different skillsets associated with batting in different places.