I agree with you; the reason their N64 output was so high (and arguably their mid-2000 era) was due to their projects getting green-lit left and right, leading to them jumping into the developmental phase very quickly them most other studios
. There is a BIG reason the N64 got 7+ Rare games after all (not counting moved/changed projects like Project Dream, Conker's 12 Tales 64 and Dinosuar Planet) XD.
With the early Xbox years, Microsoft told them "Do what you want; make us money!" and that lead to many former GC projects becoming Xbox titles (GbtG in 2003, Conker Live and Reloaded in 2005), projects being moved to the 360 for its launch (Perfect Dark Zero and Kameo in 2005) and that lead to Saburman Stamped being scrapped due to that team being dragged into helping the Kameo/Perfect Dark Zero teams get their game ready for launch.
Shit hit the fan, respectfully during 2006, where many teams were working on things:
-Conker team: Horror game pitches
-Perfect Dark Zero team: Perfect Dark Core
-Kameo team: Kameo 2, Crackdown 2
-Banjo/DKC Team: Viva Pinata and Banjo 3
-Starfox Adventures/Jet Force Gemini Team: Various other projects/helping other teams out
But every team but the Banjo/DKC team was faced with various cancalations during 2007/2008 due to Microsoft wanting Rare to make 'family-friendly' games....leading to those teams leaving Rare during the Kinect era or being layed off :'(.
The Banjo/DKC teams were content with things, as they got to make their Banjo 3 (though different then it was on the GC/Xbox) and a new IP (Viva Pinata); they just left at the right time after the Kinect era to form Playtonic and thus Yooka-Laylee was born :').
Not sure what happened to the Starfox Adv./Jet Force team, but I would likely guess that they either got rolled into the Banjo/DKC team or stuck around due to not minding the Kinect work (they never got to make sequels/games they wanted but likely enjoyed working at Rare; Saburman Stamped was their last solo project before being scrapped due to Kameo and Perfect Dark Zero needing help :'().
Right now, Rare is at a good place despite all of this bad blood between them and Microsoft.
-They can make mature games again (Sea of Thieves, hints at Battletoads coming back, and the KI revival under Double Helix/Iron Galaxy all prove this)
-Microsoft is giving them more freedom (they have four developmental barns now, so multiple projects can happen at once)
-Some people from Rare's past are still there (at least some of the Banjo team is around despite a number of them moving to Playtonic)
-Rare Replay came out; shows that this 'new' rare respects their past history and accepts its warts and all (why else would they have a few scrapped games included as videos or their more 'bad' games like Goules in the mix?)
-Sea of Thieves shows them making 'big' games again