1: Fairness towards the other racers, as if Sonic was allowed on foot, All Sonic characters would have to be on foot, including Eggman, and then nobody would win but Eggman.
2: okay, the REAL reason is that he DID at some point, but his small size and screwy mechanics made this more frustrating to work with, so they just put him in a car. Knux, Shadow, and I think Amy and even Big were supposed to be this way, Eggman's vehicle had feet, and Tails drove in the ACTUAL Tornado, which was MONSTROUS in size due to the wingspan. So yeah, probably best to just go with the car.