I find synthetic ones good for keeping my head warm in winter. Also useful riding in the rain or snow when glasses just become a blurry mess (maybe I need Oakleys?).
I wear mine on the turbo as a sweat band as well.
Never understood people wearing them in warmer weather, my head would cook. I noticed Bertie wearing one with the top cut off to create a peaked headband. I assume this keeps out the sun/rain but doesn’t keep you warm.
Also never understood why they are always cotton – we don’t wear cotton clothes elsewhere when cycling.