Nisht – fair enough. I was responding to hakohen’s assertion that a hat is Mesorah or “the right thing”. There is no such Mesorah, and certainly not for hats as worn today by yeshiva bochrim.
Further than that, if you would agree that there are head coverings that are respectful for davening other than a black fedora (which it seems you do), and that it is not a requirement for davening, I’ll take that and leave it alone.
P.S. for certain I was going overboard on the fedora point, but was doing so to show that Moshe Rabbainu did not come off Har Sinai with one. How a beged becomes or changes from a beged Ish to Isha or vice versa should be for a different thread.