I think a main point isn't being addressed, and that's that the anime is an adaptation of the games. Believe it or not, everything is set in for the games first, and then the anime takes it from there and uses the Pokémon. So a Pokémon being able to dodge in the anime (which in all honesty is kind of crap to begin with, as the battling mechanics in the games and in the anime are two totally different things) based on an evasiveness stat honestly doesn't make sense to me. It would change the whole mechanics of the game (BSTs, IVs, EVs), which would just be a pain in the butt for the developers to even work around, and have to go back and change all the previous 600 odd current Pokémon.
You could say, "Hey, they split Special into Special Attack and Special Defense in Gen 2!" But that change made sense. There was already attack and defense, so splitting Special to fit the same mold (while only changing a MUCH smaller amount of Pokémon) was reasonable. On top of that, Gen 1's mechanics were still getting refined, so IVs and EVs really didn't have much bearing on that change either.
tl;dr If it ain't broke don't fix it