Nation states in the EU follow the direction their politicians get pointed at by the money that gets them elected.
A more powerful EU would mean less power for big corporations and wealthy individuals.
Right now, "EU washing" unpopular policies is a thing. National (usually corporate) interests can make EU laws happen, and when they have, national politicians say "Sorry, our hands are tied - EU law!". So I'm not at all optimistic that the EU political organization, of all things, will reduce corruption just by getting more power. But I do think that more direct elections to powerful EU positions will improve things.