The four-move barrier have been strongly followed in the Anime since the DP series.I think that the four moves only thing happens in the games. Pikachu has had many moves and Charizard knows about six. Charizard definitely knows Seismic Toss, Flamethrower, Slash, Dragon Claw, Wing Attack, and another Fire attack but I forget which one. Pikachu knows Thunder, Thunderbolt, Volt Tackle, Swift (it used it once), Quick Attack, Electro Ball, and Rock Smash. It may not use some of them often but it still knows them as no Pokémon in the anime has ever forgotten how to use a move before.
Anyway, I would like to see Ash finally win a League someday using his strongest reserves from the previous regions.