You'd think that would work in a pinch, but I find it's really necessary to have both the neck and face shaded simultaneously. When it's 100+ degrees and cloudless skies, the neck and face being shaded at once can make the difference in being able to spend 5 minutes outdoors and 10 minutes outdoors without excessive discomfort.
A lot of black people, especially in the south, really like wearing work clothes. Every black dude I see in my town always wears stuff like overalls and trucker caps even on their days off. I guess they like it because it goes with their sense of style?