In trying to explain Why Cameras Use Proprietary Batteries, many have claimed that it is because proprietary lithium rechargeable batteries have better high-current capabilities than any AA (though nobody has linked any reputable source substantiating this) and that camera makers are greedy companies that want to force you into buying their expensive battery.
Why, then, do flagship flashes like the SB800 use AA batteries? If you've got supposedly superior high-current battery technology in those proprietary lithiums, here is the place to use it. Imagine the faster recycle times.
And if you're greedy, then you're greedy - why not take the opportunity to shaft customers on your flash batteries just like you do for the cameras?
Something doesn't add up here. What's the truth behind using AAs in flashes? (And as a bonus, go answer the original question - we should be able to develop a consistency between the two answers that explains the opposite choice made by camera makers).