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Natures currently are doing more harm than good. Individual pokemon are going to like certain accessories/foods/flavors/hobbies than others, and that's great. The problem comes from how nature hasn't been revised since gen 3, and gen 3 had a flawed implementation of nature to begin with.
The first problem with nature is that it means 29/30 of your pokemon will be born to suck, that isn't including things like abilities, hidden power, IVs, or sex. The way nature is currently set up basically demands that the best way to battle is to gen your pokemon and not even play the game. In turn, organizers tend to accept that hacking is not cheating as long as everybody looks the other way.
EVs starting with gen 3 used to have a similar problem where actually playing the game permanently contaminated your pokemon. This was fixed with super training, but nature was overlooked.
A potential side-benefit of removing natures as we know them would be to improve diversity in the metagame because dumping an attack stat would no longer be granting every sweeper a free bonus to attacking power. Natures benefit walls less because you can choose your pokemon's movepool, but you have less control over what attacks your opponent uses.