Lots of Americans like baseball and enjoy wearing things with logos on them. This seems to be particularly prevalent among Americans as compared to Asians or Europeans in my experience - in those places, people will get gussied up if going to a game or maybe a bar where the game is playing, but Americans will wear team memorabilia on a daily basis. It’s not unusual to see people wandering around in basketball jerseys, for instance. Here, in Detroit, people wear Red Wings jerseys all the time. When I was growing up, I had a couple I’d wear regularly as well. Americans like sports and readily show their affiliations with attire.
Some people just like the look of baseball caps in general. They have become associated with certain subcultures, and lots of people wear them for the style. There are entire stores in malls that literally just sell baseball caps of virtually any flavor you’d want - and they’ll make custom ones for you if you wish.
They’re practical. The part of the baseball cap that goes over your head either has elastic in the back or an adjustable strap, so they always fit comfortably. Many times the back of the cap is made of a mesh fabric, which makes them light and cool on hot days. The bill of the cap is longer than basically any other hat form other than a 10 gallon cowboy hat or a sombrero - if it’s sunny, it’s useful to have. (It’s also generally more socially acceptable to wander around in a baseball cap as opposed to a gigantic cowboy hat or a sombrero most of the time.)
Indeed, if you are having a bad hair day, a baseball cap can help. But so can any other sort of headcovering.
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