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My solution is Box Draft, which works similar to character selection in games like DotA:
-Each player fills a box of 30 pokemon with complete sets. No arbitrary rules/complex bans, anything with over 600 BST is prohibited. Everything else? Fair game. Species clause is in effect, you cannot have two different sets for the same pokemon in your box.
-Each player can see the other's box. They can see the pokemon's sprite but nothing else.
-After a few seconds of viewing, each player may select two pokemon to block out of the other player's box. Players cannot use these pokemon in the coming battle.
-After this is made, a coin is flipped to decide who picks first. The progression would be simple with ~20 seconds for each phase: ban two (both simultaneously) > Pick two (P1) > Pick two (P2) ban two (P1) > ban two (P2) Pick two (P2) > Pick two (P1) > Ban two (P2) > Ban two (P1) > Pick two, Ban two (P11) > Pick two (P2). P1 gets an extra ban phase in the last pick phase because P2 gets last pick which is a significant advantage in a draft situation where the players do not share a depleteable character pool. In theory this should even out the initial coin flip's impact on the game since P2 has more information for his last picks but has less options available to him.
Essentially, when two players meet up in box draft, they have their own meta including only the 60 pokemon between them, you no longer need to build a team to account for so many different threats, only what they can hold in their box. Teambuilding as a skill is actively utilized and incorporated into play in a much more strategic way than we see in Battlespot, where each player blindly picks 3 of 6.