Still in curmudgeon mode:
I love to see men in hats. Real hats. Baseball caps are not hats. Baseball caps belong on boys. The only men who should be wearing baseball caps are those playing the game.
I was never annoyed by the ubiquitous billed caps until I started noticing a trend. Guys who wear them don't realize that they aren't supposed to leave them on inside. I have noticed that men who wear real hats tend to be very polite. They remove them inside. They remove them in the presence of a lady. Some of them even doff them. Unfortunately, the same cannot often be said of the overgrown boys who wear baseball caps. I know a very proper young lady who met a guy for coffee. He never took off his cap. Even if he had been fantastic in every other way, he wouldn't have had a chance.
I can understand why the guy doesn't want to take his cap off walking through Walmart or Gander Mountain. I'll cut him some slack. But when he's sitting in a restaurant--white tablecloth, cloth napkins, wine list--he needs to take it off. He also needs to wear a shirt with arms. Please.
ADDENDUM: Yes, many of the men I love wear baseball caps. My favorite bald guy often wears a baseball cap. My wonderful brother wears a baseball cap. That doesn't mean that I have to like it. And if they ever displayed poor hat etiquette, I would probably confiscate the hats. (My favorite bald guy is making a transition to real hats. He looks so incredible in his winter dress hat with his suit and overcoat on!)