fyi firemen definitely do NOT wear their hats “whenever they are on duty”; those hats are for their protection not for the honor associated with the position.
Some other posters mentioned that the hat signifies someone as a “yeshiva educated” male. But what about those who are yeshiva educated but does not wear a hat because they grew up outside of a society where everyone wears one? Why would some people, even after being notified of their education and credentials still reject someone in shudduchim, or judge someone in general for something so chitzoniusdik?
And there is no way to “prove” something is objectively more respectful. The same way many years ago society dictated that wearing a hat was a sign someone was distinguished, why is it so difficult to swallow that, since society has adjusted (I wouldn’t necessarily attribute to its “decadence” any more than I would to explain why we stopped wearing powdered wigs as a sign of stature) certain people/circles have elected to adjust how they dress when they are trying to give off a put-together appearance when they daven or go about their day? Especially when one grows up in a society/ is born in an era where putting on a hat may make them feel less yirah than not wearing one?