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It's not really worth worrying about unless you're going for some kind of challenge run.
A solo-run with a bad type combination being fucked over by low IVs and a bad nature could certainly make things less fun, and you'd wind up having to cheese battles more and more to compensate, which isn't entertaining.
Although sometimes you'll notice one of your team members is doing worse than all the others, and the nature and IV check post-game usually shows why.
