For single player etc, yes it would be fun
but it should be able to be turned off for Competitive events. So everyone fights at the same level.
Then the competition is down to skill, tactics and command.
it should only be a thing if there is a singleplayer part in this game. otherwise i think the "i have more freetime because i dont have a job" thing is not very usefull. on cs.go there are too much flaming kids wich think they gained the thing of life if they reach a high rank. *just a joke..*
If you actually get butthurt by kids bragging about their cosmetics stuff, then maybe take a look at the internet in general. There's always a way to piss off others by one mean or another. Whereas cosmetic bragging isn't the worst kind of bullying.
During my 6 years playing the Red Orchestra series, I've never had a guy run up to me saying my character looks bad, because the change is subtle, and there's only three looks overall for each role depending on experience.
People are more likely to bully you because you suck at a game, rather than bullying your characters look, in games in general.
Another option for cosmetic stuff might be having some skill calculator do the math and assign you either a more ragged look or a emblem on your shoulder, its just as subtle, but then you actually got the right to brag, if you want to look like a complete asshole of course.
Making it optional to wear certain looks would also diffuse the situation, as players will choose whatever look they feel like, even if they might unlock more looks by progression.Overall, implementing player progression will, as I've said in an earlier comment, make the game more attractive and popular as you feel rewarded by playing it.
See behaviorism, pavlovs dogs, positive motivation, whatever you want to call it. It works like a drug.
Source: Myself from experience being a teacher, server & game admin and past community manager.