It's not just the DAC. A headphone must then also have its own amplifier (typically op-amp) as well since the signal is amplified AFTER it's converted to analog from digital. That needs more battery power than just a DAC. Thus, there is no free lunch. Your phone will need a battery and your headphones will need them too unless its using a powered Lightning connection (which means using a cord and won't allow you to charge and use the audio at the same time).
Of course, you have a dac and a preamp.
I was thinking of the wired scenario, the wireless scenario is... just too weird for me.
It's a horrible idea UNLESS you just happen to own a headphone company in which case you would probably love to sell Bluetooth and/or Lightning powered headphones that work directly with your new iPhone while everyone else is forced to use some dongle that they will likely quickly lose and get so frustrated that they will go buy a new pair of headphones from Apple or a 3rd party that pays Apple a license to use said Lightning connector.
This.