Here's the problem with stats for hats:
Why are there weapons with different stats now? They provide choice and interesting stuff, sure, but the real reason that they are feasible is that EVERYONE has them. Honestly, you might craft some away or whatever, but guaranteed, because of the drop system, you'll have whatever it is in relatively short order. The reason very few players complain about weapon stats (as a whole, not individually) is because no one person is privileged.
Hats are different. As many people have already said, I have [X] gameplay hours, and I only have [~X/100] Hats. Hats are rare, meant to distinguish people in a symbolic - and not practical - sense. Golden wrenches are the same way. A privileged few got them, but they are no different from the regular wrenches, functionally. Sure, a golden statue here, and a shiny wrench there, but no gameplay advantages.
It doesn't matter if hats had BALANCED stats; the point is, they give certain lucky players more options, which isn't particularly fair. Should hats become a commodity, and super easy to get, fine, but in their present state, not a chance.