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I don't think I'd mess with the structure too much desu. I'd keep:
>8 gyms
>elite 4
>Team ______
What I would do different though is have more competitive concepts in game. Throughout the game each trainer battle is there to teach/reinforce a concept used in online/competitive battling
>The first trainer introduces pivoting during battle based on typing
>another trainer uses a setup-sweep strategy
>stealth rock trainer
>bulky water types
And each one would deliberately point out what it is that thay're doing. As such gym leader difficulty woud be higher and some might use multi-tier strategies like stealth rock + roar or perish song + mean look.
I personally don't like the Team ____ aspect of the games but I wouldn't mess with the formula. I'd make them use cheap, annoying strategies like choice items on weak mons (like whatever this game's incarnation of Rattata is).
Maybe the 4/5th gym leader could be a middle form enthusiast...from china 中 and the whole gym is about showing effective uses for Eviolite.
I think it'd be awesome if the games had a high expectation of the plaers and actually taught them how to do through demonstration of metagame play styles. It might be kinda hard for kids but Fortnite and Splatoon can be kinda hard too and most kids I know are really good at them.