Here is the thing. Cosmetics are very important in a game when they enable archetype fantasies. WoW is a game with a magnificent wealth of hero character archetypes yet only allows a small number of them to be playable. Cosmetics can to some extent let you tune your character better with a desired archetype; I remember how many blood elf dark apotheosis warlock cosplaying as demon hunters existed in MoP because it was a very desirable archetype that we did not have access to.
This leads to cosmetics. Some limited cosmetics are time limited. Those same cosmetics can "click" when it comes to helping a player represent a desired archetype. Gladiator mounts and elite mogs can be quite unique, even if the latter are recolors; after all recolors can better represent a specific faction affiliation.
AS a long time RPer and GM, most game master books that describe player goals place "playing an archetype" among the top reasons people play RPGs (often either the top or right after variants on escapist power fantasy). It's human nature to enjoy playing roles and to find further enjoyment in immersion and playing them well; in a game environment like WoW that is mostly possible through customization.
So FOMO can just disincentivize a player from picking up a new character or even the game when they realize they can never really attain the archetype fantasy they are searching.
That said I don't think seasonal rewards are problematic or should be abolished. I do think it should be possible to earn them off season by completing tasks. Add a token you acquire at 2400 and then again at 3000 rating (good luck with that) which allows you to buy a different season's elite mog for your class. If they'd ever add seasonal mogs for M+ they could do the same; complete everything at +25 and you get a token to grab any past M+ mog you want for that character. If you can eventually get something, however grindy it might be and however far in the future you might get it, it still feels attainable.