For any discussion like this, it helps to know the history of first party and third party relationships, and especially how platform holders have viewed third party developers.
Atari (starting in Gen 2) - "Third parties are the enemy. They are competing with us on our own platform. The first third party company, Activision, was formed by a bunch of ungrateful Atari employees that left us and formed their own company. The rest are parasites that pump out shovelware. Every sale to a third party game is a lost sale for us."
This is before any kind of royalty licensing models were started between first and third party developers, so the two sides were antagonistic to one another. Also, aside from Activision, third party games were the worst shovelware here of any generation. Third party games definitely had a perception of being low quality games.
Nintendo/Sega (starting in Gen 3) - "Third party games are there to support the more important first party games. First party games sell the most and drive hardware sales. Third party games help round out our library and give players more games to play between major first party releases. We make royalties from third party sales and they get to access the platform and install base that we established. It's a win-win relationship."
Nintendo had changed the relationship between third party and first party developers. Now they were working together instead of against one another. However, since third party games had such an awful reputation, Nintendo had to restrict what they could make on the NES. This is why NES games had the Nintendo seal of quality on them, to boost the reputation of third party games. At the same time Nintendo limited third party publishers to 5 games per year to prevent them from churning out shovelware like they did on the Atari 2600.
I also need to point out that Sega had essentially the same view on first/third party games as Nintendo. What was the main 16-bit game that competed with Mario? It was Sonic, a first party game. Sega also saw first party games as the reason that people bought the hardware and third party games were there to support the first party games. They did actually give a better deal to EA, but this was because EA had strongarmed them into it. EA had backwards engineered the Genesis. They told Sega to give them a better deal or they would publish all of their games unlicensed on the Genesis. So, Sega conceded and gave EA what they wanted.
So, this is still the model that Nintendo still uses today. It made them successful in the past and they are still successful with this philosophy. There is really not a good reason for them to change how they see the relationship between first and third party games.
Sony/Microsoft (starting in Gen 5) - "Third party games are the main reason why our system is successful. First party games help round out the library and give players something to play between major third party releases. They also distinguish our system from the other non-Nintendo console. The AAA third party games are what gamers want most and we have built our business around that."
This is the model established by Sony. You can trace it back to the PS1 and especially Final Fantasy 7. The PS1 was not selling especially well until Final Fantasy 7 launched on their system. Sony then learned pretty quickly that they would be more successful supporting major third party games instead of competing with Nintendo directly on first party games. This is the model they have been following since the PS1, and it has worked really well for them. There is no good reason for Sony to change their first/third party philosophy just like there is no good reason for Nintendo to change their philosophy either. Both companies have been very successful following their philosophy.
When Microsoft came along they copied Sony's philosophy, so they also focus mostly on major third party games. Now that two console makers see AAA third party games as ultra important it makes Nintendo seem weird. And then this narrative gets perpetuated over the years that Nintendo has a weird way of relating to third party companies. In truth, Nintendo is not weird. They are simply doing what they've always been doing. They have not changed, but the rest of the gaming landscape has.
Furthermore, it would be foolish for Nintendo to make a serious bid at some Western AAA game like GTA 6. Let's say, for the sake of argument, that Nintendo offers Rockstar some awesome deal that would make Rockstar $1 billion extra over what they would normally get for GTA 6 exclusivity. Sony would then have to counter by making Rockstar an even better deal, because they need Rockstar to compete against Nintendo. Nintendo doesn't need GTA, but Sony does. So, Sony will always outbid Nintendo. On the other hand, since Nintendo doesn't need Rockstar to be successful, they would never really make this deal to begin with.
I use this example to illustrate the basic differences in philosophy between Sony and Nintendo. Sony does much more to cater to AAA game makers, because that is their basic business model. That is not how Nintendo's business model works, so that is why they make less of an effort.