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Jumping into the anime canon for a sec, Ash has almost if not all the badges from each region, and doesn't need them anyway as we've established a full set from any region counts. Regardless, he's got at least 30 of them. Also, Ash has taken his Pikachu on every adventure and at this point it's level for sure is 100.
Let's ask some questions:
>Why do badges let you train higher?
>How do Giovanni, Archie, Maxie, Cyrus, Ghestis, N, Zinnia, and Guzma have higher leveled pokemon and progressively higher leveled Pokemon without badges?
>How would Deoxys, Giratina, any fossil, space, tim, God, and Ultra Beast recognize the authority behind a badge?
Final reminder that Badges are canon mechanics in both anime and game, see: Ash's Charizard, the games.