There already is one of them, it's called the Ruby & Sapphire 200 metagame.
...what, you wanted something more specific? Alright then. I personally think this is a great idea, even if I'm somehow shocked the existence of this thread didn't violate any of the OI thread rules. (Seriously, this feels like it would be better in Ruins of Alph or something, but you do you I guess.) Either way, I've got some ways this could be run in each individual game.
-Available in all main battle formats with each format having a different maximum number of Pokémon per battle, just like the Battle Tower and its many variants
-Useable Pokémon limited to the regional PokéDex of the corresponding game, with preliminary bans set on masoct Legendary Pokémon and Mythicals, as well as any other event exclusive material
-Here's the big difference between this and RS 200: For a team to be registered as eligible for cartridge-based battles, they would either have to be A. the team you completed the game with according to the Hall of Fame sequence, or B. enter the Hall of Fame on a later attempt while following the previous note. Registration would be monitored by individual Pokémon, just in case one Pokémon finds itself present in more than one team.
Additionally, the parts of each game could all be their own smaller metagames, based off various checkpoints in the game. For example, a (very shallow) metagame of only early-game Pokémon obtained before a specific Gym Badge is obtained, with level caps set accordingly. Something like that. Those level caps would be equal to the level of the checkpoint Trainer's highest leveled Pokémon. (Example: 0 Badges meta level cap in RBY would be 12-14 because of Brock.)