The wii controller is constantly using (relatively) large amounts energy to measure/process/send sensor data for however long you play. A remote on the other hand is intermittently transmitting short messages. My guess is that a large amount of the energy dissipated in the remote batteries is self-discharge, which makes putting a normal battery in one a little bit of a waste.
I know there's not serious data processing on the remote, but I count an analog to digital converter as processing.
The main reason why I don't think it would be suitable for a wii remote is that two AA batteries are supposed to last 45-60 hours depending on use. Remotes last much longer. Granted the wii remote is used more actively, I still think the non-reliability issue, even if only for pause, kills it as a power source.
In the end though, its probably the consumer's decision unless nintendo hard wires them in.
The Audio comes in as ADPCM, which does need to be decompressed and then goes through a DAC plus presumably some kind of amplification. ADPCM is easy to decode, but does still need a processor of some kind.