Red and his starters are among the most recognizable characters in video game history. Sakurai felt so strongly about the concept that he put three times as much effort into the character(s) than anyone else in Brawl -- he designed three original move sets for a single character, and he went through the trial and error of getting a new mechanic to work in the Smash Bros. environment. Pokémon Trainer's also one of the few newcomers featured on Brawl's box art. He's nowhere near expendable, and replacing three original Pokémon with three new original Pokémon isn't "easy."
The most important thing to realize is that despite four generations of Pokémon games existing while making Brawl, Sakurai still went with the original starters. He could have gone with the Gold/Silver trainer, Ruby/Sapphire trainer, or Diamond/Pearl trainer, but no -- he went with the original. He was the most iconic/popular back then, and he's still the most iconic/popular now.