I'd never really though of Nintendo as innovating with hardware in order to avoid innovating on their cornerstone series. I always thought of them as just conservatives, but you're absolutely right- they keep their brands alive by adapting to their hardware innovations, not by trying to make fresh versions of old things (like Ninja Gaiden). And I didn't mean to say that I'd only like gritty reboots (although, you know, I really really would love one)- anything which shook up the formula in a meaningful way and wasn't a gimmick (Snap and Pinball come to mind...) would be great! A story, characters, just something that said "This wasn't made to be next year's garage sale, and it's not Crystal v. 3.05."
While the other games can have interesting ramifications or quirks when trying them with new hardware, Pokemon is just... not different. It doesn't make any mechanical difference whether you pick "attack" or "hyper beam" with a d-pad or a pointer or a stylus. It's the same.
This is a great point, and not something I would have thought about. As fun as it was at the time, Pokemon Stadium could never stand up on its own legs, which Nintendo seems to have realized.