I don't see how it won't improve audio quality. Phone DACs are generally low quality and inadequately shielded, introducing all sorts of noise even before the signal has to travel down the wire. A standard for digital audio and wide market adoption of digital headphones (physically separating the DAC from the phone radio) can only improve audio quality.
This may have been the case a few years ago - and maybe still in some lower-end phones - but it hasn't been true for a while at the high-end, especially in iPhones, which seem to be the first high-profile phones to axe the headphone jack. Moreover I can't imagine why you would expect many headphone makers to use better DACs - now instead of $10-20 earbuds at least being driven by a decent DAC, they get to use whatever 10-cent piece of shit the manufacturer threw in to keep the price down.