Hats for gaining the Sets?!..No - Sets for gaining the Hats!

Polycount Hats for Spy/Soldier/Scout/Pyro give you the Set and additional stats. I call it "Hats for (gaining) the Sets" (and I'll call them here like a "Hets").
Now imagine that if you complete any Set, you gain the Hat. New hat. Not giftable, not tradeable, not craftable. It's even not in your backpack. Because it's shown when you complete the Set. I call it "Sets for (gaining) the Hats" (I'll call such a Hats this way - "Sats").
Example: you choose the loadout for your Engineer: Frontier Justice, Wrangler and Gunslinger. Then you choose the option in the settings "Show the Hat when the items are in the Set"(<<Show the "Sat">>) and mark the classes. Ok, Engineer. Now, when your loadout is similar to the one above, you have a "Sat" on your Head. For example, it can be called "Engineer's Update "Sat". I don't want to imagine the example how it could look like. The one obvious thing: it's not like any existing Hat or Het, which can drop into your backpack. The purpose of this "Sat" is to show another players what weapons you are using at the moment.

That's all. Simple and good idea, I think.
P.S. Possibly, I will add examples in future. Just for fun!
P.P.S.Quick note: it could be placed into the Action Slot...