I don’t think brands should refrain from self promotion. Big brands have tactics that allow them to have access to all different parts of business that helps them reach more consumers.
For example, would Adidas stop advertising because they want to be authentic towards other businesses? No. Adidas is a big enough brand that even if they stopped promoting themselves, people would still know who they were. I think that if a brand has grown to be huge, it deserves to self promote just as much as other businesses.
I do suggest that there be a platform for small businesses that need help with promotion which can be helped through larger businesses, but all iln all big brands should not refrain from self promotion.