We start limiting ourselves by assuming too much though. Look at Melee. Every Pokemon character was featured in either the anime or a movie. Then Brawl came and we got Pokemon Trainer. In total, Ivysaur probably got....ten minutes of air time on the show?
Maybe the reason why we got Pokemon Trainer is because Sakurai thought it would be very interesting to have a character who is really three characters in one. It is like Zelda / Sheik but with a third transformation. I think it is rather fitting for the Pokemon Trainer. In the games, you are always given a choice between three starters but in Pokemon Yellow, you could have all three starters.
As for the starters, I think Charizard was chosen because it is the most popular starter of the 1st gen games. Sakurai probably wanted the starters to represent each type and each evolution stage so since Charizard is the final form and Fire-type, Venusaur and Blastoise are out. Next choice was Squirtle because it is more popular than Bulbasaur and Charmander is out by default because of Charizard. So, by default, we get Ivysaur.
I think the idea of a Pokemon Trainer in Smash was planted in Sakurai's head after he saw Ash Ketchum's name in the Melee poll results. But he didn't want to put in anime characters so he used Red instead because he's who Ash Ketchum was based on.
Still, Meowth should get in SSB4 already... like you said, every playable Pokemon was featured in the anime or the movie. Meowth is the second-most recurring Pokemon after Pikachu and as far as I know, is still appearing in the anime to this day. Of course, a playable Meowth would not be based on the anime, but rather on the games... Meowth uses Pay Day in the Pokemon games and SSB64/Brawl but cannot use Pay Day in the anime. Meowth can use Fury Swipes in both the games and the anime.
Just bring back Mewtwo and add Meowth and a 5th gen Pokemon (or a 5th gen Pokemon Trainer) as playable characters in SSB4 and I am good to go. We always get at least two newcomers from the Pokemon series. One of them is usually from the 1st gen and the other is from the recent gen with the exception of SSB64 when we only had 1st gen at the time.
SSB64: Pikachu (1st gen), Jigglypuff (1st gen)
Melee: Mewtwo (1st gen), Pichu (2nd gen)
Brawl: Pokemon Trainer (1st gen), Lucario (4th gen)
SSB4: Meowth (1st gen), Zoroark or Victini or new Pokemon Trainer (5th gen)