Well, Gen 1 does exist...it's the first game, and has the first Pokemons..
Pikachu is in every game.
I can catch a Magikarp almost anywhere.
Kanto is in four different generations.
Generations arent at all a logical way to divide Pokemon by- its an extremely inconsenquential marker that defines little of the differences of the character. People who holler about 'generational representation' issues provide no reason with why it matters what generation a Pokemon is from- color coding Pokemon is as efficient.
And for that matter, if we are counting generations, than lets exclude Mewtwo, Charizard, Pikachu, and Jigglypuff from the count, as none of them were included for their generation. It is an arbitrary and superficial way to differentiate Pokemon and the Pokemon variety, which is, quite literally, as saying 'we do not need another Pokemon whose name starts with a G.' We can play off of many tropes in the pokemon world- multiple battle mechanics, item holding, types, strategy, game genre, media of mass encounter-- but playing the generational game is an ignorant view of what is important to the series.
I think Ditto would be better in that role, honestly.
I would have to disagree; many fighting games have a character that 'takes moves' based on other characters; I described Mokujin from Tekken, but San Tsung is a similar character as well. We could say Kirby is our guy in this game, but I think it would be fun if one character kept his body, and had a moveset mostly dependent on the other character. Ditto simply transforms, his body is no different.