I don't think it's necessarily the higher MP count, but that may be part if it. Bigger image files require more computing power, which requires more juice.
For example, most DSLR cameras have (I think) one processor that handles all the functions of the camera. The latest, pro models have two or three processors...partially because of the larger images (more MP) but also to speed up the overall operation of the camera. But at the same time, I think I read somewhere that newer processors are also designed to use less power that older ones. So there would be some give and take on the power usage.
Another reason may be voltage. Their cameras may run better when they can use 7+ volts, which is easy with a lithium battery, but would require more AA cells. Also, longevity is better with lithium. I haven't really tested it, but I have battery grips that can use two lithium batteries or 6 AA cells. The AA batteries (I think) would only last for a fraction of the time (shots) that the lithium batteries would.
Also, it comes down to the spacial design of the cameras. (also true with many P&S cameras). They can design their lithium batteries with a wide range of shapes & sizes. My P&S Canon elph has one that looks almost like a CF card.