The one problem with licensed music is that the game company has to pay the author's rights for it, which could cost them a fair amount of money, and it'd only be worth paying for that if their game was extremely popular (Like Need for Speed Underground for example).
Anyway, the feature I would have for it are :
1:
Everything the old games had - Yeah, I can't decide between having all the courses, characters, design, whatever, so just include everything they had (unless they'd be planning to release the old games on the VC or something).
2:
Costume customization system - Everyone here want that, so there can't be much room for excuse about not including this. To have a even wider range of costume choices, why not separate the costumes in parts : Head, body, legs, miscs (Miscs could be for special accessories like Cat ears, Devil's tail, Angel's wings, etc.). And if you want to extend it even further, the game company could release some bonus costume sets for 2 dollars or so.
3:
Cross-Platform Online Multiplayer - In case they'd want to release this game on all three major home consoles (Wii, Xbox360 and PS3), why not make it cross-platform so you can play with anyone, no matter what console they are using.
4:
Arena-Mode - I haven't thought of this idea all the way through, but basically, it's Mario Kart's battle mode for SBK. I'm thinking about balancing it with giving the characters new stats for this mode : Health bar, Recovery time, Offensive, Defensive.
Some weapons, items and special boards might be not available in this mode for game balance, like the pans and the Ninja Board (if they'd include the old special boards in the game).
5:
Custom Course System - Pretty self-explanatory. Make your own Race/Arena Course with a various choice of unique textures, ramps and such. This might be a pretty heavy feature to implement into the game, since there could be so many things people would want to add into their courses (self-made textures, custom music, etc.), and considering the Wii's limitation (lack of harddrive support), this feature might not be possible. Maybe for the next gen console?
I might as well throw in some courses idea I had in mind (don't hit me if you got the same idea before I did

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Rocky Volcano - Located somewhere in either Crazy Jungle or Turtle Island, there is a big active volcano in which you can... "snowboard" on.
The way I'm imagining it would be having two or three alternate routes, one mostly outside the volcano, one mostly inside, and one that varies between both. Some obvious course hazards would be either lava pit and fireballs coming out of the lava as you cross a bridge or something, rockslides (outside) and Tectites.... just kidding. The only thing I find a bit bad about this course is the lava pits, it's kinda extreme for a kid game, but just make the character react like Mario or Link from Wind Waker, and it should be fine.
(Yeah, I know I made lot's of Mario and Zelda references in this course idea

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Virtual Mountain - Always managing to find new ways of experiencing snowboarding, Wendy Lane does it again by creating a course in a new exciting virtual world. The way I imagine the cutscene : The kids get invited to Wendy's house to be then transfered into Wendy's computer, and appear in the Virtual course, all of them having "tron-like" costumes.
The way I imagine the course is in colored wireframe with a sort of static background (like in Megaman Battle Network or something), maybe add in some ad panels, like "Wendy's Internet". Some unique hazards for this course could be parts where gravity is reversed, and maybe even have alternate routes you could access when switching gravity, like a vortex or something, and "firewalls" appearing and dissapearing at random on certain parts of the course, blocking you if you run into them.
And that's about all I could think of for the game. Another suggestion I would've added is "Create your own character", but I already got 5 features explained already.