The answer to this question is for the most part, the PS2 existed. I don’t think it mattered what games came to other consoles, how they looked, how revolutionary they were, or what the price of the other systems were.

The world was hyped beyond belief for the PS2.

It was the first console I waited in line for. The PlayStation had truly changed gaming and the PS2 was all but guaranteed to do the same. The hype for it was so high that it killed the amazing Dreamcast before it even had a chance to fail on its own. Even second place for the GameCube was not guaranteed as Microsoft came out with its “edgy” XBox console so there weren’t even enough scraps to go around for three competitors.

Oh, and Nintendo launched with a Luigi game instead of a Mario game. I don’t think it would have changed Nintendo’s fortunes much, but having a mind blowing 3D Mario “may” have gotten a few more casual eyes looking Nintendo’s way.

Hey, I’m a Nintendo fan, but after the N64 and the complete lack of compelling software for the system (I worked at a video store and saw all of the games that released for it) even I wasn’t that hyped on the purple cube. In fact, it wasn’t until Metroid Prime released that I actually came back to Nintendo.

So in short, Sony was on fire, Dreamcast’s fire wasn’t enough, Microsoft was quickly stealing fuel, and Nintendo’s magic had all been but extinguished in the public’s eyes.

On the other hand, the GBA was the successor to one of the best selling devices of all time, had a great library, oh, and it had a little phenomenon called Pókemon running in it as well. It was also geared towards younger audiences, an audience that Nintendo has never lost, even during their darkest hours.

The best bet with the GameCube would've been to:

- Move up your launch to November 2000 and move Zelda: Majora's Mask, Paper Mario, Perfect Dark, and Conker's BFD to GameCube launch window titles and enhance the graphics for all of them. PD and Conker barely ran on the N64 anyway and Zelda required the Expansion Pak too. Let Banjo-Tooie and Pokemon games be the N64's send off. You cannot give Sony a 18 month head start and launching alongside Halo on the XBox was not ideal either.

- Scrap the kiddie purple plastic look and make the silver and black models the launch models.

- Scrap the mini-DVD, it didn't even improve loading times and was just being different for the sake of being different. The GCN tray size could still hold a full size disc. Make DVD movie playback available through a remote control accessorie like on XBox (was also planned that way for the Wii).

- Enough with the dumb "different for the sake of being different" elements to the controller too. Give it a proper second Z button, a proper d-pad, etc.

Gamecube arrived so late (especially in Europe) had no DVD, and PS2, starting in 2002, had the GTA games phenomena and GC not. Don't expect Metroid Prime can compete to that, even being a phenomenal game even today: Switch "remade" port (is basically a port) sold pretty well 20 years later, including in some markets where the original one sold practically nothing, because many did not even knew the game or even the GC existence. By that time many media was full on PS2.

Basically if Gamecube was launched a year before (I repeat, it was launched in May 2002 in Europe. By all accounts TOO late) with DVD reader, perhaps it would had a great option to success or at least, to have a great portion of the market.

GBA had no competiton at all, literally (Neo Geo Pocket Color was already dying).

Plus, Pokémon was a total deal for kids.

Plus, GBA was compatible with GB/GBC games from day 1.

Plus, GBA SP was very nice and portable for young adults.

That's why.

The first reason (the non-competition situation) is why Sony decided to launch the PSP in 2004-2005, thinking it would destroy Nintendo in the portable market. But... Nintendo DS appeared at the very same time, and we all know what happened :)

"Why was the GBA Successful but the Gamecube wasn't"

Competition? or lack there off.
That and game library.... as much as people here love the gamecube, I personally felt it was one of the weaker libraries from nintendo.

It comes down to the strength of the competition.

The GBA succeeded because Nintendo had (and still has) the handheld market on lock. The GBA was affordable and had all the right games needed to prove to be a hit system. At that point, the most successful non-Nintendo handheld had been the Game Gear, which sold fewer than 11M units worldwide. The GBA was running effectively unopposed. It had a strong performance in Japan, putting up the second-best single-year performance ever for a system at the time in 2001. It did especially well in the U.S. It managed to beat the PS2 as the best-selling system of the year in 2003 & 2004. In fact, by the end of 2004 it had managed to almost catch up to the PS2 in LTD sales in non-aligned terms despite releasing eight months later. It was by the end of its short life the third best-selling system ever in the U.S. at the time, behind only the PS2 & Game Boy. While it was later knocked down a few ranks by the DS, Wii, 360, & Switch, it managed to put up sales during its prime that were among the best ever. If it had a couple of more years before the next generation of handhelds released, it probably could have passed 100M units sold worldwide.

Meanwhile, the GameCube did relatively poorly because it had to contend with the strongest competition Nintendo ever had. It had the misfortune of coming off the heels of the N64. Nintendo already lost a ton of market share in the previous generation, for reasons already discussed to death. The PS1 easily won its generation, outselling the N64 three-to-one worldwide. The PS2 was riding the wave of that momentum, going into 2001 with its only competition being the Dreamcast, which it was outselling by staggering margins. The GameCube not only released in the face of competition that was already that dominant, it also had to contend with Xbox. That generation's outcome was already settled before it got fully underway, and the PS2 consistently maintained majority market share. Basically, it was Nintendo vs. Xbox in a race to determine who would take the spot of a very distant second place. Xbox ended up edging out the GC worldwide, mainly because of a relatively strong performance in the U.S.

Both sold around 2/3rds of their predecessors, didn't they? Although the GB technically spanned two generations.

Pokemon. GBA had far better software support.

I thought GameCube actually had OK 3rd party support. Resident Evil 4, Resident Evil 0, Viewtiful Joe, Metal Gear Solid: Twin Snakes, Final Fantasy: Crystal Chronicles, Tales of Symphonia, Star Wars: Rogue Squadron II/III, Phantasy Quest Online (for whatever reason) and multiplat titles like Soul Calibur 2, Beyond Good & Evil, The Matrix, SSX Tricky, Prince of Persia: Sands of Time, TimeSplitters 2, Splinter Cell, Madden NFL, NBA Street, Tony Hawk Pro Skater, etc. in itself isn't exactly terrible.

There were plenty of fun games to play.

The system just wasn't "cool" enough though, the loss of James Bond is really understated as GoldenEye 007 was really important to the N64 in the West where it managed to sell about the same as the Super NES (the main loss came from Japan). And then there was the loss of "realistic Zelda", well they did get Twilight Princess but the system was effectively dead by that point so it made no difference.

Metroid Prime was too slow paced of an IP to carry a system.

Things like Animal Crossing and Pikmin weren't ready to be embraced as big hit franchises at that time, again the pop culture of the day was hyper obsessed with being "cool".

The N64 was really the first "shooter box" console with things like GoldenEye 007, Turok, DOOM 64, Perfect Dark, etc. This was long before Call of Duty. It definitely had an edge over the Playstation there, but they basically gave that away to the XBox. In a parrallel reality circa 1999 I probably tell Nintendo to go quietly buy out the studio called Bungie just up the street from NOA and make the game they're working on (Halo) exclusive to the Dolphin/GameCube. 

The main point of the mini-DVD format was to fight piracy; faster load times were a side benefit, although that mainly came from a faster optical drive and increased RAM from the PS2. But to say that it didn't improve loading times is flat-out wrong: https://www.ign.com/articles/2001/07/02/now-loading-2