I didn't say it was a problem but one of the theories for why they would make this change is audio quality. I believe it would allow you to build pre-amps and things into headphones.
Yes, you would need at least a D/A converter and a preamp in the headphone. But why would you want to do this? Good headphone DACs/amps are relatively big and heavy and they run on batteries (yet another thing to charge). The Fiio E5 is a small headphone amp (no DAC), and it's still the size of an iPod Shuffle.
And if your headphones are getting a digital signal instead of a 3.5mm jack, you can put the relatively big and heavy DAC in the headphones instead of using the dinky one built into the phone. The lightning port will also deliver more power than the 3.5mm jack.
A pair of headphones has space for something the size of a Fiio E5 (potentially several times that size), but there's no way Apple or anybody else is going to built that quality internal to a phone.
Earbuds won't have the space for that hardware, so I expect the phone will still have an onboard DAC and an analog output mode over the lightning connector for use with cheap/small lightning earbuds and to allow a passive lightning/3.5mm adapter.
EDIT: As an addendum, I'm expecting we'll see a lot of bluetooth headphones with the iPhone 7, following in the Apple Pencil's "plug into lightning to pair and charge" setup. Hopefully also using the wire for data while they're connected.
I think that's the point of lightning - they can derive power through the port. As for size I think there's already a few products out there that manage it. I saw one reviewed a few weeks ago.
There already exists a range of audio equipment and headphones that use the lightning port on existing iOS devices.