chiming in with j&working22 and the Wolf – I have been working in “white collar” suit-and-tie environments for 17 years, in various cities on the East Coast and traveling throughout the U.S., regularly interacting with board-level execs of publicly traded corporations and other professional staff – and I have NEVER seen one of them wear a fedora (the common “black hat”) of any color or style –
Hats in the U.S. went out of style when JFK was innagurated – he did not wear one to his innaguration, and American men took their cue from their young president and rejected hats from daily dress wear – it is simply no longer an accessory that denotes formality or dress – outside of “our” community, it is anachronistic and arguably may attract more attenion for its unusual character than any sense that a man is better dressed when wearing it – so, I would argue against the notion that we wear hats when davening because well-dressed men would wear a hat to meet the president/royalty/national leadership –
What I do see, however, is men wearing pressed suits, crisp shirts, and clean ties – so, I would argue that if a man wants to dress the way he would when going to meet royalty or the president, a necktie would be more consistent with general practice than a hat