I am under the impression that some hats have particle effects. If you are playing a spy who is impersonating a character with that kind of hat, the particle effects aren't duplicated.
I would appreciate it if someone who plays TF2 more than me can say how much it affects the gameplay.
The other issue, which is one of the reasons I stopped playing (aside from me pretty much stopping playing video games in general) is aesthetic overload. I don't like the notion of things being called "purely cosmetic" because appearances have meanings. The 9 classes were designed to be recognizable from their silhouettes alone, which is pretty brilliant. But now you can pile an absurd number of things onto your character, completely changing that. Not only do you not know what your opponent is equipped with anymore, you also have an additional psychological blocker to identifying them. And it's just tacky. TF2 was originally a 60s spy movie parody, and I really felt that. Now it's just... everything. It's just a lot less compelling to me.
That's interesting and quite disappointing to hear. In Valve's in-game commentary, they specifically point out that they were trying hard to achieve exactly this (distinctive outlines). It sounds like there's been a complete change for the vision of the game, likely due to personnel changes.
However, TF2 was very much on the right track to have the perfect combination of revenue generating side-items with unchanging gameplay. Just because they've strayed a bit does not mean that it can't be effectively used for other games.