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Breeding. The whole system needs to be completely reworked, because the basic concept of raising a Pokemon as your partner is rather jarringly at odds with the mechanic of breeding dozens of trash eggs just to get your Ubermensch.
We've already got ways to change IVs and EVs, now we just need some kind of 'counseling' system that lets you change a Pokemon's nature. Rather than breeding to get egg moves, there could be a sort of "joint training session" where you can have one Pokemon teach a move to another.