The loudness control on receivers and integrated amplifiers is designed to compensate for the human ear's relative insensitivity to low frequencies and to a lesser extent high frequencies at low acoustic levels.
Most loudness circuits are wired into the volume control so that as the volume is raised the loudness function tapers off. The problem is that people don't all hear the same, the Fletcher-Munsen curves developed in the 1930s were only a model of what people hear, on average but no one' hearing is perfectly average.
At really low listening levels with speakers, or headphones, the sound you hear can benefit from some bass boost, so the loudness control might be worth a try. Ideally, by the time the volume control is half-way up there should be little if any difference in what you hear regardless of whether the loudness switch is engaged but many manufacturers choose to leave the loudness function engaged for far too loud acoustic levels, so the bass really gets pumped up even when the music is already loud enough not to need this artificial boost.
Because the loudness function is wired into the volume control on most units and when using most headphones the volume rarely is turned up as high as when listening to speakers, the gradual tailoring off of the loudness function will not work as designed with headphones.
In the late 1970s Yahama had a line of receivers and integrated amplifiers with a very well designed loudness control. Instead of a switch, there was a rotary control. To use this control, first you set your volume control to where it would be when you normally listened to music. Then you adjusted the loudness contour until the bass, midrange, and treble of the music you heard was well balanced to your ear. This loudness control worked pretty well. It is really too bad no one offers such a control today.