I'd love for a DKR revision. I enjoyed DKR DS very much - and will enjoy it if Playtonic builds on the custom race editor. That was fun. Would especially be a success with crossplatform play.
I wouldn't expect the game until about 2020 as Playtonic's fourth or fifth game. There was an interview where I believe it was Gavin saying he'd like to get a second team working on another project and they can give each title about two-years' development and lead to annual releases.
But as for making a DKR type of game, I want karts. Mario Kart alone just doesn't cut it for me.
How do you recreate a kart game though? Make it like smash bros. Characters have different moves to aid them in the race. Yooka can use his tongue to grapple onto an object and make a sharp turn at high speed. Laylee can cause a nearby enemy racer to lose control for just a second (can't turn the vehicle, can't accelerate or brake) using an ear-bleeding scream.
Of course it's hard to speculate on other powers without knowing any other potential racers. But if there ever were an ice-based character who like Elsa can freeze stuff or craft ice, that could be interesting to make a slippery strip of road where you have no traction and can't turn, but you can accelerate. That iced part of the road would be usable by your opponents as well, so you can lead up to some creative moments by throwing ice down on a narrow bridge to require players to be perfectly aligned with the bridge or else they risk falling off.
Woaaaah, it finally came out!