They only appeared in Yellow, and that was because it was basically an anime promotion and a gap for the next gen Pokémon games. Pikachu is the FACE of the whole Pokémon series. Sakurai added Jigglypuff because she considered her as a "joke" character aside that she was popular at the moment (which wasn't the sole reason). Mewtwo was basically considered the most powerful Pokémon at the time aside that it was a boss in the Stadium games. I can get Lucario because he talks, and that Misty had her anime outfit. But if GameFreak considered Jessie and James as videogame characters, they would be featured more since just one game, and Sakurai would have used Ash's design instead of Red's.
I don't think Pikachu became the face of Pokemon until the show aired, I could be wrong though.
The reason Jigglypuff gained Sakurai's interest was probably because she was popular in the show.
Mewtwo had a movie right before Melee, but his stance as most powerful Pokemon might be another reason (though this is definitely not reflected in Melee).
And I think the reason why Jesse and James don't appear in the games too often is simple, Team Rocket disbanded a LONG time ago, and the game canon isn't necesarily the show canon. But I'll give you this... there isn't a Pokemon Yellow remake nor were they featured in Leaf Green Fire Red, meaning Nintendo wants them more associated with the show, and around Ash Ketchum than the games and their protagonists.
Smash Bros is not supposed to follow any sort of game canon, which makes them a bit more likely to appear in SSB than in Pokemon games. All I'm saying is they're in the realm of possibility.
I would have never expected them to give PT Ash's designs (though they sure tried to emulate his voice from the show) for the same reason I don't expect them to include Team Rocket's show designs, but Gamefreaks' art style instead (much cooler imo).
Anyway, not trying to stir things up or anything, but Pokemon type of representation is not set in stone, and in my eyes, is heavily based on the show as it is, except with GameFreaks designs (notice how Pikachu has absolutely no expressions from the anime)