I dig the battle/elimination race idea. Bring back Double Dash style too - two items is good, but two racers with strategies based on unique item usage/personal "hero" items like in the original Mario Kart is even better.
I like the course maker idea, but keep it strictly for battle mode - Nintendo's left battle mode irrelevant since N64, so letting there be a community that does that would be huge. I think that competitive racing should be strictly kept to the already finely-tuned tracks that get released, no course editor/maker.
I like the idea of additional kart styles, or expansion of the multi-type terrain. Keep going with that.
The mission mode/single player stuff from MKDS has to return somehow. Can't believe that never came back since then!
Keep it Mario Kart, though - it doesn't have to go full Smash Kart where everyone's a character (especially since half the characters who'd show up in a game like that already currently have, or have had, their own racing-style games).
Honestly, the way for Mario Kart to grow even more is through Battle Mode. More modes, different modes, and more open tracks/track styles for kart combat.