The manners on hats died when men stopped wearing them in business and formal situations. I think without the requirement of wearing them anymore, dads just didn't teach their sons the rules and it never moved on to the next generations. By the time ball caps became popular, the etiquette was pretty much lost.
Whew MAGA... they don't know the hat etiquette, nor do they know the flag code, and judging by all the terrible things they say about the non-Republican presidents, including drawing them tired up on their pickup trucks, I don't think they know how to respectful at all.
Anyway, about the cycling: no, it's not better elsewhere. In Japan they everyone rides bicycles. Yet, manners are terrible, especially for kids. High schoolers will weave in and out of traffic on their bikes, cut right in front of people driving fast, the works. If a car hits a bicyclist here, it is automatically 100% the car driver's fault, so his insurance takes a hit and he gets a mark on his driver's license, yet avoiding hitting these crazy kids is hard sometimes.
Yeah... it's not only the US.