Just something random I did, this is actually based on a suggestion a long time ago. These hats are basically something you can get from Job Instructor at 200 after a (hard) questline. These would be adventurer-exclusive but other classes would probably have something similar (just to be fair), many of which would probably be just the hot time hats with better stats.
These hats have no slots but have special "potential" just like Dojo Gloves. The hats are also "Joker Items" like the Root Abyss equips, meaning these hats will act as a legit piece of any set.
As you can probably notice they are based off the headwear of their job instuctors.