The Wii represented a major turnaround for Nintendo's fortunes after two generations of underperforming hardware.

But what if they'd made it a generation earlier, instead of the Gamecube?

In this scenario, let's assume the Wii releases in 2001 for $250, with hardware on par with Gamecube, and that it gets both titles like Wii Sports/Wii Fit, but also still games like Metroid Prime, Mario Sunshine, etc but adapting to utilize motion/pointer controls.

In this situation, how do you think history would change for that generation and the years/gens that followed, and what's your reasoning?

Well, it would have limited to no online capabilities more comparable to the actual GameCube and not Wii. Say goodbye to the Wii Shop Channel, or the Wii Menu with channels as a whole. I don't even think it would have a Mii Maker. It probably wouldn't get Wii Motion Plus, even by 2004-2006.
I have a feeling it carves a niche better than GameCube did but much worse than Wii did in real life. It outsells N64, but I don't know if it can outsell SNES/Super Famicom.

Hard to say. Nintendo tends to be very innovative in their odd numbered generations, while their even numbered generations tend to be more conservative.

Odd numbered consoles include Gameboy, DS, NES, N64, Wii, and Switch.
Even include: GBA, 3DS, SNES, Gamecube, Wii U, and Switch 2.

Sometimes the even numbered ones get it right (SNES and Switch 2)… SNES had some incredible innovations in chip technology, and also really advancing the NES interface. But N64 was their only failure in the odd numbered gens, and I think it was because they were conservative where newer tech would have been cheaper and allowed for far more storage space.

If they had the interface tech, the EShop, and the Channels, Wii would have been a very big deal. But it would have consumers asking why no DVD playback? The Wii had digital video, so if they added a DVD player, I see it having a big advantage that generation, being the most advanced console with a fresh new take on gaming, cashing in on the catalogue with the EShop, and taking 3D gaming to the next level

PS2 would still be closely aligned with powerful third parties like Squaresoft - who were a massive deal at the time. Nintendo would have still lost Rare and DMA/Rockstar North (I’m assuming).

Xbox would likely be DoA. Panasonic 3Do tier.

Pretty much this.  Although I will say the original Metroid Prime making its debut with pointer controls may have been too much awesomeness for me to handle at the time.

It would have done quite well because it would effectively be state of the art + it would have the casual appeal as well. That said who knows, there's a time for things and maybe gaming needed to get to 2006 to develop the nostalgia for more pick and play/simplified style games. PS2 era was still about 3D graphics and cinematic games showing what they could do.

There is a reason DS came out in 2004. It was the warm-up for the "casual" audience. I think DS is a key contributor to the Wii's success in what its goal was.

Was the tech for motion controls up to Wii era standards by 2001? For the sake of the scenario, I'll assume that they were.

Miis would not necessarily have been a part of the GC-Wii ecosystem, since the project that became Miis started as a project for the DS. I expect that a lot of games like Wii Sports would have suffered as a result.

A lot of GameCube era games would likely have looked very different. SSB Melee is so closely tied to the GameCube controller, I can't imagine that turning out as well as IRL.Luigi's Mansion likely would have tried to do something like tying the flashlight to the Wiimote, completely changing the game's perspective. Games like Wind Waker and Star Fox Adventures would have tied combat to Wiimote waggling. Metroid Prime would have been even more mindblowing with pointer controls.

If I remember correctly, they got the patent for motion controls from the owner who designed the system they used years after it had been invented.  There may have been production cost differences between 2001 and 2006 to the former's disadvantage, but it was possible to create a Wiimote in 2001.

Having lived through that era, the biggest thing that held Nintendo back after the N64 was that they were battling (and re-enforcing) the reputation of being a kiddie company which wasn't helped by Luigi's Mansion being one of the three launch titles.  When 2005 rolled around, there was a "here we go again..." fear from us Ninty fans when the first chatter about the Wii was about Miis and Wii Sports; thankfully the PS3's "Riiiiiidge Racer" launch took some of the heat off Nintendo and allowed them to finally break that reputation with the realistic Zelda we all wanted after OoT/the Space World tech demo. 

It may not seem like much now, but having the average age of a gamer still below 30, but rising well above 12, at the start of the century did a lot to color the market at that time.  For those who didn't live through it, here's a great synopsis of what it was like to actually live at the time (I personally saw it as a drawback from the upbeat optimism of the late-70s and 80s but others will have nostalgia for the time):

My company started using accelerometers in 2001 (in an attempt to do dead reckoning for GPS navigation when satellites are out of view) The actual accelerometers didn't add much cost, couple dollars, so the tech was cheap enough already. 

The Wii also benefited a lot from Wii Fit and Yoga was gaining popularity in 2000, Wii Fit could have been even more successful (23 million sold). DDR was still very popular, benefiting Wii Fit as an alternative, which in turn could also have pushed Eye Toy Kinetic more (2005) by increasing popularity of lounge fitness.

However TVs weren't quite there yet. 2001 we still have small CRT tubes, would Wii Sports have fared as well when crowding around a 27" CRT? By 2006 large flat screens became popular, perfect for Wii Sports bowling etc. Also aiming with the Wii pointer on a 27" tube is a lot harder than on a 50" flat screen TV. 

One other question is wireless tech. The Wavebird controller came out in 2002 using radio frequencies for communication. Bluetooth wasn't quite ready yet for gaming controllers. Not sure how that would have affected price or multi controller support.



Was the public ready for Wii Sports in 2001? That I don't know, console gaming was most popular with teens and early adults at the time. By 2006 the avg age was 30. The Gamecube was still ridiculed for being a kiddy toy, nicknamed a lunchbox.
https://www.resetera.com/threads/in-retrospect-how-justified-was-the-gamecube-is-kiddy-image.208158/

Also the GC was $200 vs $200 Dreamcast and $300 ps2.
Wii was $250 vs $400 360 and $600 ps3.

The Wii was much better positioned as the cheaper alternative, public was more ready to play console games with their family, TVs were bigger to share the Wii together, and thanks to the ps2's success, consoles had moved more into the living room (DVD/CD player).

The Wii release in 2001 without DVD would still have struggled against PS2. 
https://www.thegamer.com/playstation-2-dvd-player-best/
In 2001 DVD players started outselling VHS players, DVD was the hot new format.


In the end I don't think the Wii would have fared that well in 2001, likely following the same fate as the GameCube. Eye Toy Kinetic bundled with Eye Toy ($50) only sold about 10 million on 160 million PS2s sold. Maybe it broke the ice for Wii Sports but it certainly didn't ignite the get up and move your arms to play like Wii and Wii Fit ($90) did.

The Wii was not that much more powerful than the GameCube, so this is a viable scenario.

I think though Mario Sunshine would not have happened and we got a Galaxy style game earlier. The Wii does not have a second control stick for camera movement. I therefore think we would not have seen a sandbox game like Sunshine. The reason Galaxy is not a sandbox was the camera control in the first place.

I also think for this very reason we would not have Windwaker, I mean Twilight Princess was a compromise on the Wii. I played the GameCube version back in the day, so don't know how compromised the camera control was and if you needed to center the camera at the back of Link all the time with the Z-trigger or not, like in Ocarina. For this reason Skyward Sword has very linear path levels with the exception of the Sky and water, where the turning radius was big enough for the auto camera to catch up.

If overall the Wii would have reached the same or higher success as it's 2006 release? Hard to say, sometimes the right product just hits at the right time. Let's not forget it was competing with the launch of a $600 Playstation at the time as been the new shiny thing. It was like half the money. Against the PS2 it might have been harder to drum up the right excitement and momentum.