Can some hats and berets actually be professional?

I'm in cosmetology school and me and my teacher are doing a presentation to our principal because it's actually an all around tech school that berets should be aloud to be worn because it's not really a hat, its like a hair assesory. And there's other professions that wear hats I there career. Such as cooking class wears chefs hat. It the 70s nurses used to wear little white hats. Do you think that hats should be aloud to be worn in a professional environment if worn correctly? It can dress up any bad hair day! Or cover your roots when you'd pushing that last week before you have to color your hair again.