Powering the bluetooth radio takes some power (more than driving the DAC and amplifier for headphones).

> carrying two cheap sets of headphones around doesn't sound more convenient than just using wired headphones

I actually carry three: the one I use every day, the spare for that one, and the other one that's more comfortable but lacks the volume for use during my commute.

This is not a big deal if you carry a satchel or purse or backpack or pretty much anything bigger than the pockets in your clothing; all three of them, plus charge cables and manuals, fit in a hard-sided case that's about the size of a can of Skoal, and which very conveniently came with the first Bluetooth earpiece I bought. If I didn't have such a preference for entirely in-ear monaural models, they'd take up a little more space, but only a little.

It's totally doable and not even inconvenient - this latter, in particular, not something which can fairly be said of wires.

Apple's posted stats are 50 hours audio playback on the 6S over wire, 40 hours audio playback on the 7 over Bluetooth. I can attest that on my 7 the bluetooth can run down the battery a bit, but nowhere near as much as wifi, cellular or screen. How much battery drain you see in practice is probably affected by which headset you're using, what standards and codecs it supports, and if the iPhone can (presumably) burst AAC audio to the headset or not. I really should get around to reading a book on the bluetooth spec to better understand this stuff, though.

What bugs me about the iPhone 7 is that I expected if Apple was removing the headphone jack that they would add USB type C and Bluetooth 5 instead of the same-old lightning port and 4.2. In fact, it looks like there's more than one model of iPhone again, and the 6S' support for both CDMA and GSM appears to be a fluke, or they couldn't do it in time with the new antenna design. Unless I'm reading the iPhone LTE specs page incorrectly...