You do realize certain headgears will cause the hood to go down on many of the robes.
No they don't. They cause it to disappear completely. And then your character has a cross between 80's nerd sunglasses from "Sixteen Candles"/cyclops' visor/ and an amateur boxers headguard. Or a weird hedband that Abba might have wore. Can you picture any of that stuff on Obi Wan Kenobi? No?