Why /wouldn't/ the Anime follow a rule that's in every verse..? It's just how things are. I think 4 moves are plenty
But its stupid !
I mean, Diglet live its entire life digging But it can't no longer Dig anymore if he forgot it to learn a 5th move!!!
Or A pokemon with Big Jaw can't Bite anything if he forget ''Bite'' to learn another move!
A pokemon with Big claw can't scratch or Slash anything without learning any Slash-based attack! And it can't learn any 5th attack without replacing that slash-based move or any other 3 move.
This type of Logic only make sense in Game , Not in Anime or Real life.
Also , Alakazam said to remember everything in world but it can't remember a 5th move !
That Why Takeshi Shudo never followed 4-only attack limit because he believed it to be too Stupid.
Plus The Game & Anime clearly said that A pokemon can't megevolve without Keystone , Mege stone & A Strong bond.
Yet , The Anime screw this law by megevolving any Pokemon whenever they want without any keystone , Mega Stone or any strong bond. (Mewtwo , Diancle & Garchamp)
Plus , Trade evolution was canon in game & Anime but all Ash's rival & Jessie evolve those pokemon without trading.
Also Silgoo can't evolve though Artificial Rain from ''Rain Dance'' But the Anime screw that.
If the Anime going to screw the critical & confirmed law of the game then there is no point to follow something stupid as 4-only attack limit ! Just think , Any move we liked might get replace to maintain this stupid 4-only attack limit ! I say ''Screw this and let Pokemon learn limitless attack like the Original series''.