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.