Typical flash batteries, e.g. Eneloop can hold their charge on the shelf for a year. This would seem to make them suited for cameras as well. So does not Canon use AAs for their cameras as well? Then we would have only one charger, one kind of battery that we could freely spend on camera and/or flash.
The Eneloop-style batteries (called low self-discharge nickel-metal hydride battery, LSD NiMH
) are a fairly new item. They've only been around since 2005. They are based on NiMh technology.
One issue is current capacity and current draw. With AAs, you have a defined package that must always be designed for. A custom battery allows the engineer to remove more than half of the packaging, and for the same current capacity, make a significantly smaller battery. OR, they can make a much higher capacity battery fit in the same space.
For example, it would take 4 AA cells to make up the 7.2v that my 7D runs on. 4 AA cells would take up more space than the LP-E6 cell, meaning the grip would have to be larger, or they would have to package things differently.
Another issue is how fast can the battery pump out the current. This is what makes the difference between Alkalines and NiMh batteries in point & shoot digital cameras. My old Olympus P&S would eat up Alkaline AAs, but using Lithiums or NiMh let it shoot for much, much longer before the batteries needed to be changed.