Not wanting to let you evolve Pikachu because it's their mascot is easy since it at least has a non-normal typing and requires an item to evolve, plus it only has one form it evolves into.
But considering that Eevee is basically becoming a secondary mascot next to Pikachu, that approach to not make people want to eveole it either does not really work out the same as it does for Pikachu. It's a normal type, and well known as the "Evolution Pokemon", having multiple different possible forms it can evolve into. And on top of that, some of them like Umbreon and Espeon will automatically happen just from getting high enough friendship through normal gameplay, or Sylveon with enough affection and knowing a fairy move that they learn naturally. And then there is Glaceon and Leafeon which depending on the game your current location would also cause that if they level up there. Not wanting to evolve a Eevee because mascot reasons is not the same as not wanting to evolve Pikachu because of mascot reasons.
I wonder if they are eventually going to go with some type of Arceus Plate-like scenario where you can equip Eevee with an item to make it temporarily evolve to that type as long as the item is equipped.
But I can also see them not wanting to do that because then it would considerably overshine Pikachu and make everyone want something that versatile on their team. Maybe if it's only something you get post-game, but that still has the overshine Pikachu problem, especially since it even has an electric type evolution.
