Yup there's nothing wrong with KSR, it's very good visually, gameplay is fine, level design is good, the avatar creator is even impressive... the only "problem" for me is that it went for a competitive design, instead of the previous "fun and party" orientation ; in the end it has less appeal. Well it worked as long as I had people on my friend list playing it, but that didn't last.
As far as I'm concerned, I'd rather have Rare work on a new IP, and focus on the charm and silliness they usually put in their games. But that's because I don't really care for their older franchises, and (most of) those can still be handled by other studios.
Banjo is not a franchise I'd trust others to do well though. 3D collectathon is a genre, that was only done right by very, very few developers: Nintendo EAD, Rare and Acclaim Austin. One could argue that Ubisoft Montpellier got it right, but since most of Rayman 2 is super linear, they couldn't make use of the advantages this sub-genre offers over "skill platformers" and Naughty Dog made a good collectathon in form of J&D, but not only was it a lot weaker than the aforementioned efforts, they also didn't really get how to properly use collectibles to structure the game world and thus this game was best when it didn't try to be a collectathon. So I really don't know who to trust with a new Banjo game other than Rare themselves.
Regarding
Conker: They'd need to have a british developer as the lead, absolutely preferrably Chris Seavor. I doubt an american studio could quite hit the nail in the humour department. At least the platforming aspect should be a bit more easily gotten right, because Conker is a very linear "skill" platformer rather than a collectathon, something more studios are capable of delivering on.
So both of these franchises should definitely be handled by Rare themselves. As for
Perfect Dark, Jet Force Gemini, Kinect Sports and Viva Pinata, I think there are a lot of teams who are experienced with shooters, simulations and kinect games, so that they could get it right. Kameo is a bit delicate as it is a Zelda clone, something only few studios attempted and only very few studios besides Rare were successful, still, it's not as rare to be gotten right as collectathons.
Diddy Kong Racing starring Banjo could probably also be developed by Sumo - they are also british (so same kind of humour), are experienced with fun / arcade racers (Sonic Transformed) and lately made some work on open world racing design too, which would be helpful in working out the overworld. Since Sumo is already working with MS, I'd actually like to see it happen, but if it does, please retain the approach of a track based game with an interesting overworld, instead of going all open world.
So, in a perfect world (for me), Rare would develop Banjo and Conker (joint effort with Seavor's studio), Sumo would develop Banjo Racing, 343i would handle Perfect Dark and JFG (they would probably be happy to not be limited to Halo all the time) and Kinect Sports is being done by one of the Kinect studios MS has once each generation and then Rare could fit in some new IP, Blast Corps or Kameo whenever they are having additional time in a generation or a great idea.