That the most powerful wasn't the most successful is more of a coincidence than the actual cause. Also, perception has a lot to do with it. Some consoles were perceived to be stronger earlier in the race than they actually turn out to be at the end.
NES... well there wasn't a lot of competetion
SNES... debatable, some people will say the Genesis had a better library
PS1: yes
PS2: yes
Wii... no, it's library is easily the weakest of all current systems if you're not a Nintendo fanboy and enjoy many genres
I think there's a false equivalency here. There are a myriad of factors that affect a given console's performance, which include: power, price, date of release, industry buzz, etc. And we don't yet have a comprehensive enough data set to determine which is the most important.
However, one thing to note is that the least powerful console is usually the cheapest. But look at the current situation: Wii U may be the cheapest, but it has absolutely no buzz in addition to not being that cheap relative to its specs (thanks to the tablet). XO's got the expensive Kinect, which means that PS4 may come very close to price parity.
Anything can change, but right now it looks like Sony's got the upper hand.
What's the implication here? That raw power in a games console is a hindrance?
EDIT: There's no mystery this. Build a compelling platform foster a steady stream of software and features that are desirable to a broad spectrum of customers and you'll be successful. Simple. But difficult to execute. Always has been. Always will be.
the implication seems to be that sales are more important than anything else (more exclusives maybe? or lead development?), but this generation proved conclusively that they are not.
OP sounded like they were just looking for examples, but, to me, the implication is that games == success, not raw power.
EDIT: Welp, you said it better than I, actually. More to it than just great games. A strong library goes a long way, looking at the DS, PS2, and 3DS, but there are definitely many other factors.
Atari 2600 VS Intellivision, Colecovision etc.
NES VS Master System
Game Boy VS Game Gear, Atari Lynx
SNES/Genesis VS 3DO, Jaguar, Neo Geo
Playstation VS N64
GBA VS Ngage
PS2 VS GC,XBOX
DS VS PSP
3DS VS PSVita
Wii VS PS3, 360
But there has to be a correlation between the power and capacity of the hardware and success in some sense. The platform inspires people to believe in the promise of certain kinds of software. Developers / Publishers are given the platform to create certain kinds of games not previously possible.
Games are still dependent on capability of the hardware to which they are made. There's a certain law of diminishing returns for sure. "Good Enough" trumps "Better".
The right answer is probably a mixture of all things.
NES beat Master System
SNES beat Genesis
PS1 beat Saturn and N64
PS2 beat GameCube and Xbox
Wii beat PS3 and Xbox 360
DS beat PSP
3DS beat Vita
Gameboy beat all handhelds produced in the 90's.