Well we have seem the "most support ever for a Nintendo console" every gen as much as "best E3 ever" from MS every year this gen.

Those just seemed like half-assed attempts to me.

The way I see it is that Wii/GC, whatever it is called, wouldn’t have launched without a revolutionary controller. When the GC was launched, it was basically because the N64 failed and they needed something out to compete against the PS2. It was one of the few times Nintendo was reactionary, the other would have been the quick DS launch (which IMO, looked like an early model, while the DS Lite is really what they would have gone for). The GC was not a well thought out machine: first, it lacked the sort of controller advancement present in all other generations of Nintendo consoles, it didn’t play very well with some established Nintendo franchises and so we lost some franchises (like Street Fighter, which would have been on GC) and many others were simplified (especially combo-based games like SSX) with content and functionality taken out. Additionally, the discs were still too small for what was required - even Skies of Arcadia Legends had to lose some of its quality (audio) as a result, could bigger FF games have arrived on the console with proper storage? Especially post-Enix merger.

Any way. I figure that WiiGC console would launch later since Nintendo probably wouldn’t have to react against the Dreamcast or PS2 at that point: especially with Square, Capcom, Enix, and Konami as exclusives/near exclusive. Who knows? There’s even a good chance Nintendo would still have Rockstar North and Rare.

I think Gamecube/Wii launches in 2004 (or late 03) with a bit of an uglier model. 2006 Wii-Lite launches with DS (what we came to know as DS Lite in our timeline), and I also see it as being between Wii and Wii U power, HD capable.

One thing I forgot to mention was the Guitar Hero revolution would have occurred exclusively on Nintendo consoles instead of first on PS2, and then moving mainly to Wii (the Just Dance games, are to an extent, related to that).

I also think that while Nintendo did have issues with third parties, they would remain onboard because there would be no Square to lead them all astray as they did in real life... I’ll say Square was absolutely right to do so, Nintendo was HORRIBLE to them over the cartridge/CD disagreement.

Anyway, on the controller, Nintendo’s always been advancing their interface, sometimes for good or bad: NES brought the D-Pad, SNES brought the diamond face buttons and the shoulder buttons, Gameboy brought portability, N64 brought the analog stick, Virtual Boy brought VR. GBA and Gamecube were really the only only ones that didn’t try anything revolutionary. I think both were stopgaps that we’re premature, Gamecube because of the N64’s failure and strong competition, the GBA because the Gameboy was suddenly popular but they didn’t have the DS ready yet and GBC tech was WAY behind. In this timeline, GBA would still be a stopgap, but with a longer lifespan due to the fact that no PSP means Nintendo can wait, but the opposite would be true for GC/Wii, Nintendo instead has their home console in need of a premature launch - this the 03/04 Wii/GC launch with ugly controllers and perhaps a bulkier box.

Well, I'm not so sure about importance of controller in timeline that has successful N64CD as pretty mainstream red ocean console. PS2 launched in 2000, and even though PS1 is less successful in N64CD timeline, Nintendo would have to release a console that goes against PS2. But that console is successor to N64CD, so it has solid hardware, just like RL GC, but DVD as well and great 3rd party support that comes from success of N64CD.

As for controller, dual analogs are by that time standard and, if RL is anything to go by and 4 generations of various configurations of it, there would be no need for reinventing the wheel. In the end, I see Wiimotes as solution for blue ocean strategy, which in this timeline is probably auxiliary and not primary goal, since Nintendo is still main (or close to main) shark in post N64CD red ocean.

Let's be clear.  Microsoft entered the market to "stop Sony".  Bill Gates did not want Sony to have a computer in the living room, which is what the PS3 originally was.
https://www.gamesindustry.biz/articles/2013-02-07-ex-microsoft-vp-xbox-was-to-stop-sony

With that in mind here is how I see each generation playing out:

Generation 5 - Japanese third parties, especially Square, all stay with Nintendo.  Sony still gets Western third party games like Tomb Raider and the GTA series (although the latter will not really be important until generation 6).  Sony also gets EA, because EA has always hated Nintendo and always will.  The Saturn still has the same fate.  In the end Nintendo wins with Sony being a very strong second place.  Nintendo wins Japan and NA, but Sony gains a slight lead in Europe.  Platform totals are something like Nintendo 80m, Sony 55m.

Generation 6 - Microsoft does not enter in generation 6, since Sony didn't win generation 5.  Sega has the same fate with the Dreamcast.  Nintendo decides to have mini-discs again.  This drives a few Japanese third party games to PS2, but not all since the mini-discs have enough space for most third party games.  Meanwhile the PS2 is still a DVD player and the Grand Theft Auto series still takes the world by storm.  Sony decidedly defeats Nintendo, but Nintendo does much better in this reality, since they keep most Japanese third party games and it is mostly just a 2-way race (after Sega leaves the market in the same way with the Dreamcast.)  Platform totals are something like Sony 140m, Nintendo 60m.

Generation 7 - Microsoft witnesses the domination of the PS2 and craps their pants.  They release their first console in this generation, but they do it a year after Sony and Nintendo, just trying to get their first console out there to learn the console business.  This generation is the first Nintendo home console designed with Iwata as CEO, so they still go the Wii route.  This alienates third party companies mostly the same way that the original Wii did.  PS3 also launches at the same stupid $500/$600 price and sells slowly at first.  This generation plays out mostly the same except Microsoft does somewhat worse and this benefits Sony but also Nintendo somewhat as well (since in our reality the 360 was trying to be the "family console" for a while too).  Nintendo narrowly wins.  Totals are something like Wii 115m, PS3 105m, XBox360 50m

Generation 8 and later continue to play out like our reality.  In the end Nintendo is Nintendo, Sony is Sony and Microsoft is Microsoft.  In spite of one key move changing things in the past, these companies still have patterns of behavior that they are going to fall into, and eventually things will end up like our reality again.