Yeah, I'm not sure why I'd want that on my headphones themselves. I just set it to a neutral EQ during initial setup, and now I change the EQs elsewhere in the audio pipeline (music app, mixer, etc) just like we were all doing before the advent of headphones with their own apps.
None of my headphones have firmware to update. They connect with copper (8000BCE) wires (1830CE) to a 3.5mm jack (1950CE) based on a 1/4" phone plug (1890CE). Some of them use neodymium (1885CE) magnets.
If I want equalization or convolution I apply them upstream shortly after decoding.
The EQ settings should depend on what you device you are using to listen - your headphones or your phone's internal speaker - according to their natural response curves.
I don't think major music listening apps will switch your EQ automatically settings based on your listening device. So either you are doing that manually every time you switch devices, or you set your headphone EQ directly.
In any case, the software around this is not clean, and has lots of room for improvement.