Third party support depends on it. Gameplay is influenced by it. Engines are built around it. It's also a selling point.
Third party support isn't coming even with stronger hardware, that is a reality most people should be able to see clearly and there is plenty of examples for it... Gamecube being the easiest to point to. Wii U itself is another actually, since it isn't seeing last generation titles that came out after its release. GTAV, Bioshock, Tomb Raider, Dead Space, Crysis 3, BF3 and BF4. Heck even Madden is going to miss Wii U, hardware isn't the issue with any of those titles. Crysis 3 was already working on the platform when EA said "No" to Crytek.
All gameplay that currently exists on both PC and last gen consoles, every idea we currently have can be explored with Wii U, no issue exists. This isn't the first 3D console or the first programmable shader generation, it even supports GPGPU. There is literally no limit to game design, only presentation.
Wii U runs just about every engine out there, and CAN run others, the main issue is EA and Nintendo had a falling out and they are the major developer who has backed away from Nintendo (no other major developer was even at the table that doesn't support Wii U currently)
It's a poor selling point, as Xbox(og) and Vita have shown us.
If it weren't for the Wii attracting casuals, who knows where the sales could have been in the face of PS3/360. Certainly having the worse graphics is hardly favorable.
Even in your handheld example, PSP saw alot of games that wouldn't have come to DS. It was also the first real challenger to Nintendo.
The first real challenger to Nintendo was GameGear, Neogeo to a far lesser extent, Wii U however holds no limitations similar to PSP and DS.
The console that had the biggest impression (before the Wii) won. PS1 successfully pulled off 3D. Genesis had 16-bit dominance till SNES arrived. PS3/360 combined have outsold Wii and are still selling.
If PS4/720 sell out at launch, it's only going to get worse for Nintendo.
This is clearly debatable, for instance PSX did not sell well until 1997 (FF7's release) the real reason it won the generation was not a wow factor that Nintendo had locked down a year earlier with Mario 64. It was because of game genres and N64's complete lack of 3rd party support, RPGs which were hugely popular at the time had no place on N64 but were abundant on PS1 and lead to a healthy ecosystem for that platform, but these things didn't happen until after N64 had already launched, before this, PS1 sold 7 digit figures in a year iirc.
Genesis also lost dominance not from power but features, the SNES could display transparencies and mode 7 was impressive for the time. Sega's main failure though was a lack of supporting their hardware properly, they always adapted Add-ons instead of featuring key software for their platform.
PS3 and 360 have certainly outsold Wii, but neither platform has outsold Wii in hardware or software.
Wii U couldn't realistically do worse than it is, especially with software coming out on the platform later this year, no matter what PS4/XB3 do.