The karts are the real playable characters in Mario Kart especially given they tend to have more unique stats than the peripheral on top that probably supplies their power source by a usb outlet that occasionally detaches (tricks). You've never seen them outside their karts.
I wonder if some character ever died in Mario Kart and that's why we don't ever see it in the roster, considering the only rescue system on the roads is fishing rods with a tiny ass string.
If there's ever been any fatal accidents in the history of Mario Kart, I'm sure the organization behind the kart tournaments is prepared by having plenty of 1-Up Shrooms at their disposal to revive any dead racers when necessary, because unless you're a generic enemy, non-recurring boss enemy or an important plot character for a one-off game or other such being across the Marioverse, you don't truly stay dead from my experience with the Mario franchise.