"That is all anecdotal and from the top of my head, not checked or researched, but I believe it to be a fair description of the last three generations."
I wouldn't say it was unfair, just incomplete. The N64 was difficult to develop for, and games were relatively expensive next to the PS1, with which I honestly believe Sony took the old MS position of "we don't give a shit if you pirate this." It gave them massive market share because half the games people bought were copies from the local car boot sale. I knew people who bought a Playstation and then never gave another penny to Sony, but they sure as hell weren't spending money on an N64 instead. Kind of ironic when you consider that the Playstation was a spin-off from a development project with Nintendo. The console that beat the N64 into the ground was their own fault! D'oh!
The GC was roughly the same power as the PS2, IIRC. Where Nintendo went wrong (and did again with the GameCube+, sorry, Wii) is not including DVD playback. The PS2 released at a time when DVD was very much desired, but the players were still expensive. It was the same price as a player or cheaper, and more importantly, it was £100 cheaper than the X-box. Lots of people bought it because it was two devices for the price of one, had really impressive backwards compatibility with the PS1 catalogue, and was a genuinely great console. It went on to be the biggest selling console in history, so I don't think that was down to power, or the Xbox would have won out.
The Wii is just a GameCube with a gimmick attached. From what I remember, the What it did was prove to console makers how strongly the public will latch on to a gimmick, so they all started including them. These days, to me, the Nintendo strategy appears to be: take something popular in the early 90s, give it a graphical overhaul, add gimmick, release, and I'm just utterly tired of it.