Ever since Sword and Shield added the "Mint" items, there has been a difference between the nature listed among the characteristics on the summary screen, and the "nature" for the purpose of modifying stats. Notably, the berries that have the effect of "gain some HP and then possibly get confused if you have the wrong nature" (Figy, Wiki, Mago, Iapapa, and Aguav) all look at the innate, characteristic nature rather than the mint-modified stat nature.
As such, there is an infinitesimally small bit of added utility in letting every single Pokemon have a neutral nature as its innate nature, and applying the mint on top of that to get the stats that you want, because then no matter which of those berries you might accidentally consume, none of them will be able to confuse you. It's slightly more relevant for Pokemon that use any of the moves Bug Bite, Pluck, Trick, Switcheroo, Thief, and Covet (plus the Pickpocket or Magician abilities)--for anything else, the only way it can make a difference is if another Pokemon decides to Fling one of those berries at you. It's extremely unlikely that you'd ever run into this--the opponent would need to desperately want to play for causing confusion while using a Pokemon that doesn't have any other move to inflict it, and they would need to have the further stroke of luck of picking the right berry that corresponds to the opponent's nature when they really need it. That can't happen if you're diligent and use a nature for which there is no "right" or "wrong" berry.
One other niche case is when you're using extremely low-level Pokemon. Nature gains and losses amount to 10% of the raw stat, which will often be a fractional number--in this case, the size of the gain in the boosted stat will be rounded down (for example, 10% of a 359 stat becomes 35.9, but that rounds down and the nature adjustment is only +35 to get to 394), but the size of the drop in the impeded stat will be rounded up (so 10% of 132 is 13.2, but that gets rounded up to 14 and drops the stat down to 118). Level 1 Pokemon tend to have stats of 5, 6, or 7, and 10% of that results in a change that's less than 1. As a result, the minus-natured stat will lose a point, but the plus-natured stat will not gain a point to offset this because the gains are too small. A neutral nature will therefore leave all the stats the same, and anything else will lose 1 point without compensation (and it can't be in HP, of course). Granted, most of the strategies you'd want to use a level 1 for make your stats completely irrelevant, and it won't really matter if you lose a point or not, but if you ever get into a mirror match, it could...
