Headphones are important for many reasons. Better being able to hear faint tones, and battery life are the ones that are tops for the detectorist.
There are other reasons to use headphones in public spaces. When people go to parks etc, they really don't want to be hearing the beeping of a metal detector.
I know for sure when I am at the beach, I have to muster all of my self control not commit a hate crime when some inconsiderate a-hat is walking down the beach with a metal detector, no headphones, and the volume jacked up all the way. I go to the beach to hear the sound of the surf - not the sound of a metal detector beeping.