Wii ended right when it should have.

WiiU marketing was the problem. People were over the Wii. They shouldn't have marketed it as the Wii's direct successor, because it made people think it was an add-on for the console they had already stopped using years prior.

The PS3 early sales are what they are though too. That's not really an opinion.

Where is all this love/appreciation/benefit of the doubt there, if it supposed to exist it sure as heck didn't benefit the PS3, 3DS all that much. 

4/6 of the systems people consider "most successful" come from a history of having a predecessor that wasn't well supported for even 5 full years (let alone 6/7/8).

1. PS2 - predecessor had long support

2. DS - predecessor had less than 5 years of good support

3. PS4 - predecessor had long support 

4. Wii - predecessor had less than 5 years of good support

5. XBox 360 - predecessor had less than 5 years of good support

6. Switch - predecessor had less than 5 years of good support, will obviously rise up this list. 

The only 2/6 examples that had long good support from their predecessors are Sony systems. Biggest failures Vita, Wii U had predecessors with fairly long cycle support, biggest mid-tier disappointments, 3DS and XBox One also had predecessors with long support cycles. 

You can't really debate any of that stuff.

The last Nintendo hardware system that was a large success succeeding a prior system with a long product cycle is the Game Boy Advance which is now almost 20 years ago, so they've had serious issues following up on systems with long product cycles for several decades now. 

Even Sony's long tail support is really because they have so much 3rd party support, it's not really Sony themselves doing much for these systems once the successor releases. There are a lot of people that just want to play like FIFA every year and don't necessarily want to buy a new console, Sony is the main benefactor of that. 

Wii's specs weren't a problem for either first or third party support. Nintendo were clearly comfortable building games to that spec, while games like Modern Warfare 3, Rayman Origins, de Blob 2, Conduit 2, etc in 2011 showed third parties could also easily make games for it if they wanted. But why would they when Nintendo themselves stopped properly supporting the platform?

Wii's specs had nothing to do with Nintendo moving on prematurely. 

SNES was well supported up until its replacement and even got significant games after that like Donkey Kong Country 3 and Kirby's Dreamland 3.

It still got major games after its replacement and strong support in its closing years, very different to the Wii.

Switch predecessor, 3DS have good lifetime support. Switch has TWO predecessors. 

SNES - long predecessor support

GBA - long  predecessor support, short lifespan, but great sales

3DS - long predecessor support, best selling 8 gen portable. 

This predecessor, has good or bad support that has a minor impact on the next generation.  

I don't think Nintendo rushed the 3DS or Wii U because of Sony/MS, because why not in that case just wait until 2013, the Wii launched alongside the Playstation 3 without much averse effect.

They had grown accustomed to very high sales the prior 3-4 years, likely pressure from shareholders to maintain that was the key pressure they felt.

Shareholders don't care the reason why sales drop, they just know they were seeing declining sub-20 million shipments and weren't happy with that. If tomorrow iPhone shipments started dropping Apple would have the same issues with their shareholders. Once you set a high bar, the expectation is to maintain it all the time. Shareholders get greedy.

Other issues hit Nintendo hard too. Game development once you get past N64 era (PS2+ tier) becomes more complicated, up to PSX/N64 style games you can still make a lot of games with fairly small main teams, but there's a visual fidelity (more polished 3D capabilities) that occurs when you go to PS2 tier or better. That made game development on the 3DS slower. And Wii U having PS3/360 tier was also another problem as that was even more complicated.

Balancing both systems likely was always going to be impossible for Nintendo.

Other factors like smartphone gaming taking off like a rocket very quickly ... by late 2009 it was still in it infancy but by late 2011/2012, it was everywhere and even tablets like the iPad were massive, massive mainstream hits popping up in households everywhere. That hurt both the 3DS and Wii U, the 3DS because it's lower end style of gaming suddenly looked out of a step with free games on a nice iPad that could do 100 other things better, the Wii U, well all the home stuff the tablet was supposed to do (Sports channel, web browser for the living room, etc. etc.) suddenly looked laughably antiquated.

They bet the farm hard on Nintendogs + cats being an evergreen driver for the 3DS that would drive sales like Nintendogs did for the DS early, and same thing for New Super Mario Bros. U + Nintendo Land for the Wii U ... but all three of these games let them down hard. They waited too long for a Nintendogs sequel, the audience for that had moved on to smartphone gaming, NSMB was too much retro 2D Mario, it was unique the first couple of times, but Nintendo had milked it too quickly with the 3DS also getting NSMB2. Nintendo Land was a decent enough quality for what it was, but mini-game collections weren't selling hardware any more by then either.