"The advantages of having the DAC chosen and tuned for specific headphones will improve sound quality"
No. All it does is increase cost for the headphone. This cost has to be kept under control, so the parts used will be dirt cheap, and sound quality will suffer. You choices will be limited as well.
If what you descibed was the norm, someone would come up with the brilliant idea of separating the transducer (headphone) from the DAC and amplifier. Perhaps putting the latter near the actual battery and logic stuff in the phone, and connect them via a long thin cable to the transducers. Brilliant!