It's the only one of their many IPs being used right now. Nintendo got many IPs that they're not using as well, who could guarantee you that they would hold Rare's talent there, when a lot of them left under their partnership.

Most of the core members of Rare had already split or were on their way out by 2002 so it wouldn't have mattered much.

If Rare had stayed with Nintendo they'd be like Retro and would probably just be doing mostly Nintendo IPs these days.  Remember, Nintendo were the ones who took an original idea from Rare (Dinosaur Planet) and forced them to shoehorn the StarFox franchise into the game instead.  Dinosaur Planet had the ability to be a "Zelda killer" when it was first shown off on the N64, but turning it into a StarFox game ruined the direction of the game, and the StarFox elements just felt tacked on.

Nintendo turned it into SFA because the project ran into problems and was not progressing like many of Rare's projects in the late 90s, they had the concepts but struggled to pull them off with out supervision and someone holding their hand in development.

That's not entirely true. Rare's charm was that it was entirely independent creatively.

Goldeneye MP for example was done without Nintendo knowledge until the last minute.

Rare had everyone in their studio, from composer to designer, everyone had their pitch in their games. They didn't need publisher's direction before 2000.

It's very true as Nintendo had to monitor them a lot through the late 90s often having to step in, when ever Rare had freedom the projects would either run into problems or have a prolonged development an example was their project Dream which members the of Conker team said was not very good in fact Rare's creativity during the N64 was inspired by Nintendo themselves as Banjo came into being due to them seeing Mario 64, before that Dream was essentially a Crash Bandicoot clone.

I honestly believe so. Not to know MS or anything, but their internal studios have a bad tendency to go from great to terrible between game releases. Rare had some good runs on the Xbox brand, but after 2008, when they started doing exclusively Kinect titles, they just hit rock bottom. I have high hopes for Sea of Thieves, but I don't think Rare will ever be like they were back in the N64 days.

I don´t think Rare´s situation is Nintendo´s fault.
The previous Rare owners were too impressed with the enormous ammount of money MS offered for the company to turn it down . Nintendo couldn´t, at that time, match that offer, for whatever reason they had.
And they wouldn´t share the developer with a rival company.

Nintendo would have been better off if they kept Rare.

Project Dream turned into Banjo Kazooie, which originally was a blueprint for Sea of Thieves. Where did you get that idea thet Project Dream was Crash's clone? Nintendo had the best 3D platformer at the time, why would Rare copy Crash?

Rare had a tremendous record for being efficient and deliver quality titles from Snes era till N64. More so than Nintendo itself. 

Nintendo was offered the company before the Stamper brothers looked elsewhere. They could've bought it for a reasonable amount of money before the auction between MS and Activision.