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.