Nintendo had no part in it. Rare was the one searching for a buyer because Nintendo didn't want to give them more money. Microsoft did. In the end, Nintendo let Rare keep all their IPs as a sign of good faith. 

This is not exactly accurate. Nintendo and Rare had a deal, in the mid-90s, Nintendo had bought a 49% stake in Rare.

The Stampers controlled the other 51%. Fast forward to 2002 and the Stampers were looking to retire, so they went to Nintendo first to sell them the remaining 51%.

Nintendo refused, that's when the open bidding began. Microsoft paid a ton of money for Rare, they sure as hell were going to get all the non-Nintendo IPs (IIRC initially Nintendo tried to have that not be the case, but MS was offereing so much money, that it wasn't an option).

Xbox also killed crash bandicoot

.

Instead of that we get Banjo Kazooie nuts and bolts....yay!

Hindsight being what it is, I would've gone to Rare and done the following in late 1997 --

Insisted they make another Bond game. If they wanted to make a game called Perfect Dark with aliens and what not -- great. Greenlight that too. But a new Bond game is for Nintendo, and fast track that for the 1999 holiday season.

Perfect Dark could continue on development as a GameCube launch title, as the game barely ran on the N64 anyway. 

Sometimes you gotta lay down the law a little bit as a publisher/owner, you can't just let the designers make whatever they want. It's like letting inmates run the asylum. A game like GoldenEye comes out of nowhere and sells 7 million copies? Not making a sequel to that would be like not making a sequel to Donkey Kong Country, just not good business.

In the long term it would've been good for Rare too, because a new Bond game for November 1999, probably could've crushed another 5-6+ million plus and that would've sealed the deal on Nintendo keeping Rare for the next 5-6 years IMO. So Rare wouldn't have had to have dealt with the crappy Microsoft era where most of the employees left anyway.

Killer Instinct (borrow that MK DC engine)
Wizards & Warriors (modern day WRPG)
Jet Force Gemini 2 (!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!)

Conker!!!

Kinect Sports was far more fun than Wii Sports.

Me thinks Captain Hindsight here needs to crack a history book.  First of all, EA bought the rights to make James Bond games in 1998, so even if Rare wanted to, they couldn't make another Bond game.  Perfect Dark was for all intents and purposes a successor to GoldenEye, just with an original theme instead of being based off the Bond license... and it ran just fine on the N64.  The mandatory use of the expansion pack allowed for much crisper visuals, nearly a dozen computer bots in multiplayer, and a co-op / counter co-op story mode way before modern shooters started doing it.

As for Rare leaving Nintendo, you're barking up the wrong tree here because simply having another "Bond" game wouldn't have changed that outcome.  By 2000, many key figures at Rare had already departed (who later formed Free Radical and did the Timesplitters games), and Nintendo started becoming a bit too controlling with Rare... Conker's BFD was born out of frustration with the family-friendly approach of Nintendo and the way their console was viewed by most gamers as the "kiddy" console (Nintendo wouldn't even advertise Conker when it came out), and their original IP Dinosaur Planet was supposed to rival that of Zelda and be the N64's swan song but Nintendo, specifically Miyamoto, insisted that Rare shoehorn the Starfox license into the game because the main character looked alot like Fox, which changed the game completely.

By the time M$ came along and made them an offer, Rare had already asked Nintendo to purchase the other 51% in the company and own them outright, and Nintendo declined because they felt it was too expensive.  You can't blame M$ for Rare's track record over the past decade either... before they became known as the "Kinect Sports" guys they currently are, Rare released a string of mediocre original titles and underwhelming sequels like PD Zero and BK Nuts and Bolts, so Rare have only themselves to blame for ruining their once untouchable status in the industry.