PS2-Tony Hawk, Spider Man, Medal of Honor, Madden, Need for Speed, Crash Bandicoot, Guitar Hero, Lord of the Rings, Star Wars, The Simpsons, James Bond, Lego, FIFA, True Crime, The Matrix, WWE, Hitman, Splinter Cell, Burnout, The Sims, Call of Duty, NBA Live, Harry Potter, Mortal Kombat, Prince of Persia

All these franchises had an entry that sold in the multimillions.

So these games were the deciding factor when it came time to choose between PS2/GC/Xbox? Most of these appeared on all three consoles back in the day too. When we take out franchises that showed up on both PS2 and GC we end up with this...

Guitar Hero

Yep. That's right. Gamecube was only missing one or two franchises (and probably less than six games) from the 3rd party western dev corral. Lack of western 3rd party support didn't doom the GC. It was the fact that it couldn't play DVDs, and that the PS2 was a similar yet better console. That and Xbox ate up a lot of Nintendo's customer base. 

You really hit the nail on the head there. People forget that the N64 had trouble because Sony took all of Nintendo's Japanese 3rd party support.  PS1 and PS2 sold well because of Japanese 3rd party support. The western devs played a much smaller role in Sony's dominance. Don't believe me? Name a key western 3rd party game on PS1 or PS2 not developed by Rockstar. Xbox had all the best western 3rd party games, and they got their buts kicked during the PS2/Xbox/GC gen. 

The sad thing here is that many western 3rd party devs closed their doors during the 360/PS3 gen. During the XB1/PS4 gen the ones remaining are playing with microtransactions, premium editions, and day one DLC. 

Switch just needs Namco Bandai, Sega/Atlus, Capcom, Level 5, Square Enix, and Falcom for 3rd party support. They just need these companies putting a serious effort into good 3rd party games. So far Sega/Atlus is working on SMTV, Capcom could bring MHXX west, Level 5 still loves Nintendo, Square Enix has Octopath, and Falcom just need to bring YS/Trails to Switch (probably an easy port job). 

I know I'm probably preaching to the choir here, but this post isn't just meant for you. It's meant mostly for all those "Nintendo needs western 3rd party support" haters. 

Edit: Here you go kiddos. I've listed all 3rd party western games from 2017 that got above 79% on Opencritic minus PC exclusives and Indies. This is what Nintendo haters think Nintendo "needs" to be competitive. 

X-Com 2 (We have Mario x Rabbids though)

Injustice 2 (ridden with Day 1 DLC)

Pillars of Eternity Complete Edition

Assassin’s Creed Origins (Day 1 DLC and Microtransactions)

Destiny 2 (Microtransactions, Splatoon 2 is better)

Shadow of War (Microtransactions)

Prey

Look at what you said

"Name a key western 3rd party game on PS1 or PS2 not developed by Rockstar"

Thats what i did, i provided a list of a whole bunch of multimillion selling western 3rd party games on PS2.

If you really dont think these games sold a bunch of PS2's than idk what to tell you. A game doesnt have to be exclusive to be a system seller.

Now you are welcome to disagree with me and this is all my opinion. But after carefully observing the Switch over months I have concluded that it's a fad that will wash away painfully soon. I will admit that it offers a great concept but without a substantial 3rd party support it will have the same fate that the WII U had. Thus far the Switch has enjoyed great AAA 1st party exclusives such as Zelda and Mario releases but if we think about it Nintendo never had to suffer with the 1st party support, they have always had strong 1st party backing and as much as I hate to bring this up again, they need huge 3rd party backing from Activision, EA, Ubisoft etc.   You may hate COD, Battlefield, Madden, Assassins Creed etc. and a lot of Nintendo fans will naturally not pay too much attention to those titles however in order to target the massive amount of casual consumers Nintendo needs support from those giant publishers.  EA has recently announced that aside from a FIFA port they have no desire to publish any of their AAA games for the Nintendo platform,   Activision has refused to even comment on the possibility of brining COD to the Switch (can you imagine how great of an idea it would be to play COD on the go?   DOOM is fantastic on the Switch). Ubisoft and other major publishers have also been rather unenthusiastic about the Switch.

Therefor, I am convinced that the Switch is a fad that will go away within a year or two. And I am not a hater by any means as a matter fact I want it to succeed because i believe it's a very unique concept, however with lackluster 3rd party AAA support it has a very predictable fate.

I'm not denying that these games sold PS2s. But why didn't they sell Gamecubes? We hear over and over again that all Nintendo needs to be successful is to get those sweet 3rd party western devs on board. And yet they did that with Gamecube and still lost. 

It's about as bad a fallacy as when people claim that Nintendo just needs a console graphically on par with PS4/XB1 to be successful. Gamecube did it. It didn't work.