The pilot hat has its traditions from the nautical profession and airship days as does the rest of our uniform and many of the rules of the air and aviation terminology. A peaked hat is a symbol of authority and professionalism, hence the police, military, merchant marine and many other rank based trades wear it. The hat also easily identifies the flight crew. Those that are concerned about passengers harassing them after a flight, wear a hat, you may be surprised the affect it has.
If they are to do away with hats as part of the uniform then reform the entire outfit, wear a plain business shirt and be called flight manager and assistant flight manager or wear the same uniform as the cabin crew. Airline management would appreciate the pilots being brought down a level. Besides there are many hat making families that depend on the business....