http://shmuplations.com/supermariokart/Freshly translated interview from the Japanese strategy guide
That’s why, during the development, it was decided that no one would be allowed to testplay the game in 2-player mode. That was something the whole staff agreed on actually. In a 2-player race, it’s the competition itself that is fun—overtaking your opponent with skillful cornerning, for instance. That’s why, when we were making Super Mario Kart, we were very careful not to lead ourselves astray in understanding what makes the game fun. We focused our efforts on the 1-player experience: if that was fun, then 2 players would automatically be fun, too.