Pikachu was popularized because of the anime/manga and Pokemon Yellow was based off of the manga.
Pikachu was chosen as the mascot before the anime began airing, it was up between Pikachu and Clefairy but Pikachu was more "boy friendly", there's an ongoing manga with a Clefairy as "Red"'s starter Pokemon though.
Jigglypuff was chosen because of the anime. She put people to sleep and drew on then throughout the first season.
It was part this and partially because she had an identical skeleton to Kirby, making her a pretty low effort joke addition, if you look at the two of them in 64 you'll notice Jigglypuff has a ton of shared animations with Kirby, and still does today.
Mewtwo was the first badass legendary, but Mewtwo strikes back sort of solidified his place in the roster.
Mewtwo was the first last boss of the series, but saying it got in Smash
because of the movie is kind of out there considering it's status as a legendary.
Pokemon Trainer was originally intended to have the 3 final evolutions of Kanto, but they decided to have the 3 evos represented: Squittles is popular due to anime
I have literally never heard of this before today. Them all being final forms doesn't even make sense from a character design standpoint. It's way more likely PT having a first, middle and final form was the plan from the beginning due to it fitting the gimmick of representing evolition way better. I also simply cannot see Venusaur as a proper fighter.
Lucario I can't quite account for, though he did get a movie.
Lucario was chosen as Gen 4's poster Pokemon, it got a cameo in Gen 3's PMD as the ultimate rank, then a movie, then appeared in nearly all Gen 4 promotional material, had an NPC ingame (Riley) who gave you a Riolu egg and finally was used by Cynthia in the last battle. Ingame it had unique typing, a signature move, and amazing base stats, it was SUPPOSED to be strong, cool and powerful. Gamefreak deliberately chose to put it in Smash because they were banking on it selling merchandise.
As for Greninja, Sakurai
stated that he chose Greninja because of his design but I simply cannot buy that. Greninja had all the red flags that Lucario did, it had amazing base stats, a good typing and a unique and totally busted ability that keeps it in OU today. Ash also got a Froakie with some epic sad backstory early in the XY anime timespan and it was treated as his ace from the beginning, implying that TCPI planned from the get-go that Greninja was going to be endgame.
I agree if they are going to pick Pokemon They should stick to the game, but you can't deny the anime affect
You have it backwards, things appear in the anime because Gamefreak/TCPI wants them to be popular both in and out of the game. This is the main reason people can see why Incineroar would be the Pokemon rep if we get one. TCPI has given it multiple spotlight episodes in the anime as if to say "Hey! Incineraor is popular! Buy his figures! Buy his Pokemon card deck!", if he gets in Smash it will be because of TCPI dictating so,
not because of the anime. The anime has been used as a promotional vehicle for the games since like...Gen 2.
EDIT: I think the only Pokemon who's gotten in Smash thanks to the anime is Pichu, and he was a low effort clone.