The sound of many headphones can be improved by applying equalization (EQ). The problem on a smartphone is to find a way to apply EQ globally to all sound.
On Android, there are some apps that can do this, like Poweramp Equalizer, Wavelet or Sonarworks SoundID, however in some cases manual work and developer knowledge is needed to give special permissions.
On iOS, it seems no 3rd party app gets access to the global audio stream and the only solution I found people use is an external hardware DAC with EQ support.