Contrary to popular opinions, what people choose isn't indicative of what's good. Pokemon Trainer is triple effort to learn (more really because you have to learn his unique mechanics on top of how to play three characters). This has absolutely zero impact on his real quality. It's absolutely zero. However, it has a big impact on the choices people make because people make irrational choices all the time (not the least of which involves the characters they pick!). Maybe they just plain don't like one or more of the Pokemon. Maybe they have no vision and can't understand why the unique training mechanics are helpful (Underrated mechanics in a smash game? No way!).
It's also unfair to the mains of other characters. I don't have strategies to defeat Squirtle, Ivysaur, and Charizard persay. I have strategies for the Pokemon Trainer. Everything I have ever learned about fighting Squirtle assumes Ivysaur comes next. Everything I have ever learned about fighting Ivysaur assumes Charizard comes next. Everything I have ever learned about Charizard assumes Squirtle comes next. One of the main things I factor in when playing the Pokemon Trainer is that he can't stick to one Pokemon forever so, if I'm having trouble, I try to minimize damage and pressure him into running out of stamina and switching. It's not the same thing as learning how to fight Ganondorf because he used to be so bad you could do anything and win. At least then, you are learning strategies that work for a general character that has always been there, and what you learn to fight him here WILL help you against him in standard Brawl (if you can beat Balanced Ganon, you'll crush regular Ganon). Here, you're basically adding three new characters to the game, characters you have to fight in a really fundamentally different way from their original conceptions. It's just not good design and a terrible approach for a character who was designed from the ground up as a team. As Thinkaman said earlier and very well, it would be homogenizing the cast. We want to have the characters as different as balance allows! Why would we make a radically unique character more like everyone else if he can be balanced with his uniqueness?
I should be clear that I don't expect all characters to be equally popular even if they are equally good. Some playstyles have wide appeal (notice how having a sword and being good instantly makes any character popular, with the suddenly interesting Link and Ike getting tons of attention). Others are more niche (how easy is it for you to get excited over being slow and campy and living forever like Samus and R.O.B.?). The extremes are Pokemon Trainer, Yoshi, and Ice Climbers who require a ground up different approach from the rest of the cast to play well. You probably aren't ever going to secondary any of them because they are too much of an investment to be anything but a main, and they'll always be a lot less popular than the other characters. That is not a problem for me, and it doesn't contradict any goals of this project. As long as those who do choose to use them aren't facing a significant handicap, even if those people are few and far between, all is well.
Also, honestly, there are two characters who work as a team via character switching and 34 who don't. Why not learn one of the other 34 if you dislike team mechanics?