I see this as an incredibly ridiculously slim possibility. But if it did have USB C I MIGHT (again, MIGHT) even be ok with removal of the 3.5mm jack. The lightning cable does nothing (havent compared spec for spec but this will remain true for most customers regardless) that the USB C doesn't do. Meanwhile it's just a prorietary port that requires special hardware or cables to use. Haveing USB C on iOS, Android, Windows Phone, etc. would be spectacular.
The USB people would certainly like to see USB-C as the new standard for headphones.
Apple has large presence in the USB Implementers Forum, it's easy to see Apple's hand in the USB-C connector.
USB, Lightning and Thunderbolt are converging. There is a USB3 capable controller behind the Lightning connection in the iPad Pro. It's easy to see Apple go USB-C everywhere eventually.
If they remove the headphone jack then the cost of wireless headphones (bluetooth and NFC) should come way down so that more people can afford to adopt.
NFC is mostly useless for headphones, it's short range. By design. It can give some convenience for pairing, but that's all. Bluetooth 4 has some features that try to take some the hassle out of pairing.
The only thing that makes cost really go down is mass production. But mass production of new stuff will not happen if old stuff, that is already in mass production, and so cheaper, is already good enough. Deadlock.
A powerful manufacturer can break this deadlock.
Wouldn't be the first time Apple did this.
But...
Can wireless headphones be good enough for enough people?
The laws of physics being what they are, wireless will always be worse for audio than wired.
Also I think it would be good for Apple to adopt NFC. Seems like every other smartphone has it.
The bulk of Android phones, the cheap ones that the carriers give away with their plans, don't have NFC.
Apple adopted NFC, but so far only for payments, the only thing that NFC does now that is not a gimmick. Apple is an NFC Consortium "sponsoring member", just like for example Google, Intel, Mastercard, Visa, and Samsung.
NFC is not particularly modern or high tech, it's used for payments because banks are careful and slow and prefer old, tried and tested legacy tech. Also, with payments, NFC's short range is a good thing, for many other uses it's not.