The main reason was because during the Rainbow Road level, playing 2 players replaces the regular 4 Thwomps with 2 Thwomps, allowing a gap to consistently drive through instead of risking smashing into a Thwomp. I missed the beginning too, but I would imagine there are advantages to pulling out a character so you can't get hit by their character-specific weapon (Peach drops a mushroom that shrinks you, slows you down, and allows you to be run over by opponents at a huge time loss, for instance). Plus, it's one less opponent to worry about, right?