Uh..that's some revisionist history there.
The PS2 was far and away the most powerful system at release in 2000. It's 2001 lineup (FFX, Gran Turismo, MGS2, Devil May Cry) absolutely buried the best the DC had to offer. Sony's PR machine was on full blast with how advanced the PS2 was, even spreading that ridiculous story about PS2's being used to launch missiles by saddam or whatever. Yes, the Gamecube and Xbox were more powerful, but by then the PS2 had the market virtually to itself for 2 straight years and it was too little too late.
The PS1 is an even worse example. The PS1 launched in 1994. It's competition was the sega saturn, the atari jaguar, and the 3D0. two of those were rendered irrelevant IMMEDIATELY as they couldn't handle 3D anywhere close to what the PS1 pulled off, and the PS1 easily outclassed the saturn in that area as well, despite being $100 cheaper. The PS1 being "weak" is flat out wrong. The N64 while a more powerful system didn't launch until late in 1996- once again leaving Sony with nearly 2 straight years to run up the score with no significant competition- and even then the N64's lack of multimedia capability let sony give the appearance of still being more powerful with advertisements full of CGI that wouldn't fit on a cart.
Momentum in the marketplace is a thing. It doesn't matter if nintendo releases an NX console that outclasses the PS4 next year or not, the thing has built up too much of a lead to reverse.
The NES? What was the NES competing with at launch? The US gaming industry was in shambles. The Atari 5200? The Intellivision? It destroyed both by a mile. The sega master system didn't launch until a year later in the states...if you could find one. Nintendo leveraged it's stranglehold on retailers and third parties to prevent games being made, and retailers from carrying it. The game boy also had no significant competition for the same reason.
The Wii is the sole example of power not mattering- and that didn't last all that long before the bottom fell out of that market.