oh look you have an XBO or PS4 =P

Nintendo games like Mario Galaxy, Twighlight Princess, Xenoblade and Metroid Prime3 pushed the Wii, so we'll assume Nintendo games on this new system will push it.  The NSMB games have been on the weak side, but SM3DW is pretty impressive (though I think it could be moreso), Pikmin 3, DKC, MK8 and X are solid graphical efforts.  This next gen system will be far more powerful and Nintenod dev teams will be told to make games that are far more impressive, visually.  The Mario team in particular will be told to make something that was as stunning to see as M64 was in its debut, and will be encouraged to "break the mold" in terms of the Mario style and theme - but not the core classic gameplay.

Nintendo will make every effort to make the system 3rd party friendly (whether 3rd parties get on board is unknown) and will push the system in marketing and with games to make the point that this is a "core" gamers system such as launching it with a Xeno-rpg and a Retro shooter game (maybe Metroid, maybe something with more mass appeal).

Friend codes are already gone and we'll assume Nintendo makes every effort to make the system have a full featured online experience.  Since they're charging a subscription like everyone else now, you also get free downloads from the eShop.

It won't support Bluray, but will display in 4k, and support all major streaming video services such as Netflix. 

They can "beef up" they're consoles ask they want. As long as they continue to make nothing new they're doomed to failure. Wii was a gimmick and many called it from the beginning. Gimmicks are successful but never last forever. The other two console makers launch new IPs to success or fail. Other than moving toward motion controls Nintendo has played it safe with both hardware and software and now it's caught up with them.

Seeing as the Gamecube was one of my favorite systems, you better believe I'd get it. Nintendo could definitely still make really interesting and innovative games without a unique built-in hardware mechanic. They could even make the thing have compatibility with the gamepad, and just come with a pro controller, and it'd be even better. Not every game would support the gamepad fully, but it would at least allow for a lot of off-tv play, while Nintendo could be sure to support it so that both control schemes would be supported, letting gamers that like the gamepad use it, while not forcing developers to add something to the Nintendo versions of games not present elsewhere. People who don't like the gamepad could stop bitching, while we'd probably end up seeing the same amount of support for the gamepad as if the gamepad were the only choice. When a developer chose to actually use the gamepad, you could count on it to be a unique experience instead of a obligatory slapped on one. And something twice the PS4 at the same price? Who wouldn't get that?

I think it would be great if Nintendo introduced a super-powerful system sooner than later and it could use the Gamepad as an optional controller.  If they were to release a mini Tablet portable console in the near future as well, the new system could use either the Gamepad or Tablet as a controller option while having something less complex come in the box.

What would they like to say?

If it had high end specs I doubt I would buy it for that. Better specs don't translate to better third party support for Nintendo.

I would buy it for Nintendo games.

Nintendo fans would buy a cardboard box with the Nintendo me on it, just ask Michael Pachter !

....and yes, I´d buy it

...but again: the obligatory gameplay > graphics needs to be said

Please show me those bare minimum efforts !

don´t make me post pictures of Pikmin 3 and 3D World and X gifs to proove you wrong !

"You never bought me!", with a sad face.