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Here's my "one change": scrap it.
Go to 15 or 25 (or whatever) types. Each type is super effective to half of them and ineffective to the other half. ... Or supereffective to a third, normal to another third and ineffective to the other third; they just have to be equally distributed.
This way, no one type dominates, you can still pick your favorite types and also becomes a much better game of "rock-paper-scissor" than it currently ends.