Errr, are you serious? N64 and Gamecube droughts were so bad that there were months with literally NO new game releases. I’m not talking only bad games, but nothing at all being released. You could literally pay attention to every game released on the console because the release schedule was a literal trickle. Gamecube was even worse because most of the third party games it did get were vanilla factory churned multiplats like Madden and Tiger Woods button based golf. The release schedule was so bad that you fans were forced to pretend that Rogue Leader and Eternal Darkness weren’t shit games (I know, I was there, I’d pretend online like these games were fun, but deep inside I was crying of boredom and horrific game balance and bland design). Whenever a decent third party game did come along, like RE4, a better version was already on the horizon (in this case for PS2 and Wii).

If anything, droughts were completely the reason the N64 and following Gamecube failed. For every game released, it seemed the PS consoles got anywhere between 5 and 20: and they were getting all the fun ones. While the dream team games were good on the N64, there simply weren’t enough of them. By the Gamecube era even the dream team and decent second party releases were gone. The 2006-2007 year on the Wii was the first time since about 1996 (a full decade) that Nintendo had a solid year of releases.

Errr, are you serious? N64 and Gamecube droughts were so bad that there were months with literally NO new game releases. I’m not talking only bad games, but nothing at all being released. 

Hm, that's an interesting statement but it doesn't make a lot of sense when you talk about the Gamecube in this respect. The Gamecube sold almost as much total software as the Nintendo 64 (208.57 million vs 224.97 million) despite the fact that it sold 11 million consoles less, and the attach rate for exclusive game series that appeared on both consoles was nearly the same from Nintendo 64 to Gamecube (meaning that Nintendo couldn't rely on the sales of these games to come close to the N64's total software sales, since attach rate is relating to total consoles sold). 

Gamecube's total software attach ratio was a whole 3 games higher than the Nintendo 64's too, even though exclusives were contributing less to total sales. And Gamecube's software attach ratio wasn't that out of the norm relative to other consoles at the time. 

PS2's software attach ratio - Around 10.7 games per console 

Xbox's software attach ratio - Around 11 games per console 

Gamecube's software attach ratio - Around 9.6 games per console 

PS1's software attach ratio - Around 9.2 games per console

N64's software attach ratio - Around 6.8 games per console 

Of course when you talk about a Nintendo console and relate it to a Playstation or Xbox console it should always taken into consideration that the Nintendo console will have a higher percentage of it's sales come from exclusives, but the point is that even with exclusives having a similar attach ratio - and thus selling worse on Gamecube than on Nintendo 64, the system still was very close to matching Nintendo 64's total software sales and ended up having a much higher attach ratio of overall software despite relying on exclusives left to make up that total. So the only logical conclusion is that, yes, third parties released on Nintendo and they were bought. 

Also, Gamecube's first year of release is absolutely filled with well respected exclusives (many third party) - though it does vary a bit based on region I suppose. I seem to remember however you stating a couple of times that Nintendo's Gamecube Era games were not very well made in your opinion, so I can understand that outlook. Nintendo 64, Gamecube, Wii, and Switch all had very great first years in terms of exclusives, and that's saying a lot because the Nintendo 64 launched with like two games. I think when you look at something like Gamecube, the biggest problem release-wise was that so much of the notable software was in it's first two years and not a lot after. 

Basically, R&D4 produced the most successful titles, and thus won the favoritism of Yamauchi. As a result, he put more focus on the now renamed EAD division, rather than focusing on growing the other studios within the company. Yamauchi didn't give all the departments a fair chance, instead he just put all the eggs into the basket of the division that got his attention the most, which happened to be EAD. The other studios just couldn't compete with Miyamoto and his team, and thus were sadly treated as afterthoughts. 

Part of the poor sales of N64 games can be owed to their obscenely high prices.

Part of the reason PS2 generation games sold in abnormally high volumes was because they were dirt cheap to manufacture and certain third parties (EA, Activision, and their like) routinely over-shipped, and that gen was the heyday for when games sold in bins like these:

It was also, perhaps, the first generation where people began buying lots of games and not playing as much as half of them (or was that just me? I know I can't be the only idiot that did that!).