That, bad marketing, a bad name, and an interface that was essentially a lame predecessor to the Nintendo Switch.

Same goes for the Gamecube too; nothing against games like Luigi's Mansion or Super Monkey Ball, but they're hardly system sellers compared to the likes of Mario 64 or BOTW.

Oomphf I could not disagree more with this. Yeah LM was no Mario 64 nor BotW, but TBF most launch titles are a Mario 64 nor BotW.

Luigi’s Mansion was a fine launch title (esp when SSBMelee and Pikmin released mere weeks after launch). Not only a highly creative and original title, utilizing gameplay mechanics never really used prior in gaming, but it also was a graphical marvel for its time. It’s like what Cyberpunk 2077 was for the Switch 2. This is nowhere in the same ball park as something like NSMBWiiU which was released under a crunch and, among other things, was confined to NSMBWii assets due to lack of time.

Don't me wrong, Luigi's Mansion is a very good game, but it was clearly not a system selling killer app like the games on this list, and that shows in the Gamecube's poor sales performance.

A bigger part of that was the PS2 only selling more because it could play DVDs. Kratos is a screaming douchebag who doesn't have Mario or Donkey Kong's lasting appeal.

Four-way tie between Mario 1, Tetris, Wii Sports, and Breath of the Wild.

Not only were each of those titles so vitally important to the success of their respective systems, but they came at crucial times for Nintendo, some of which were make or break periods that would shape the company's future. To the point where without any of them, Nintendo may not be where they are today and there may not even be such a thing as a Nintendo Switch 2.

Yep, pretty much this.  All depends on how we define "greatest".

By this rationale I voted for Super Mario World.

Best is Super Mario World for Super Famicom/Super NES. It's a classic that changed the game. The Switch version of Breath of the Wild is a runner-up.
The most important is probably Super Mario Bros. for the international NES. It made Nintendo a juggernaut.

Definitely comes down to either Mario 64, Wii Sports, or BotW.

All three of those were hugely popular and fantastically fun games that were the peak of mega system sellers. And all three felt like something completely new - Mario 64 for just being the first legendary 3D game on consoles and moving the biggest gaming mascot into 3D incredibly well, Wii Sports for showing off a whole new way to play games and was endlessly fun especially with friends/family, BotW because it gave players open world freedom unmatched by any other game before and resurrected the greatness of the iconic Zelda franchise which had got quite stale in the previous two entries.

SMB, Tetris, and SMW all get honorable mention for being fantastic games and system sellers but I just feel they aren't on the level of those other three, although SMW comes very close and could arguably be added to the first list.