It is interesting... maybe they have vision and great ideas...

Gamecube/Switch is the vision

Wii was the great idea

They stick to their vision (in the end) but cannot not release great idea

There's much truth with this post. Of course you can see some long term vision in all the products Nintendo has released over these years, but I don't agree every element was pre-meditated.

Of course I believe Nintendo had been looking to make a console that works both as an handheld and as an home system for a long time. As rightfully stated by the OP Gamecube a Gameboy connectivity and even the Gameboy player are a proof of that.
I also strongly believe the WiiU was internally an attempt to test waters for an hybrid console to come while counting on the Wii brand popularity to sustain it, only Nintendo overestimated it by a long shot.

In fact on the WiiU you could see for the first time home console games built on the foundations of portable games, like Mario 3D World based on 3D Land foundations and Mario Kart 8 which is basically an evolution of Mario Kart 7. Super Smash Bros was basically built form the gorund-up to work both on a home consoles and on an handheld.

On the other hand the Wii and DS didn't go directly into that direction, although they pursued the long term goal of lowering the expectation on graphics while focusing the player attention on other elements of the game experience.

Imo the only time when Nintendo used a real "gimmick" to catch the attention of players, is when they decided to sell the DS successor on the concept of stereoscopic 3D, while going quite against their own vision of the Wii and DS. 

Sure, knock yourself out.  If you do make a video, let me know when it gets posted.  I'd enjoy giving it a watch.  Have you made other gaming videos?

Actually, making cost effective hardware has always been on Nintendo's mind.  Gunpei Yokoi's philosophy of "lateral thinking with withered technology" is proof of this.  "The Nintendo way of adapting technology is not to look for the state of the art but to utilize mature technology that can be mass-produced cheaply."  The monochrome Gameboy released in 1989 is a perfect example of that philosophy at work and predates any notion of Nintendo trying to lower costs only after the N64.

The difference is, that in the "2D era", when developing games wasn't expensive, the cost of hardware was relatively much larger concern than it is in the "3D era", where biggest problem is the resources needed for developing a game. It would make much more sense to have separete home and handheld consoles, if you could make enough games for them. 

Yeah.  The huge sales #'s of the Wii tempted them too much to incorporate the name into it's successor.

As for the 3DS, I actually created a thread recently that addresses this.

http://gamrconnect.vgchartz.com/thread.php?id=234115

Saved.