So I pretty much had to buy a PS3 to get experiences that if the Wii were more powerful it probably would have gotten anyway.
Probably not. Gamecube was a beast and third parties largely ignored it. The few ports it did get were often half assed and even ran worse than the PS2 version. There's no reason to believe they wouldn't treat a more powerful Wii the same way.
And how much do you think such a console would've cost at launch anyway? Sony and Microsoft both sold their systems at a loss, so I can't imagine this hypothetical Super Wii retailing for anything less than $400. So whatever appeal the Wiimote had would've been moot since the mainstream would never dish out that much cash for a game console, so Nintendo would neither have marketshare nor third party support.