While driving the headphones, sure - I'll believe that in certain cases with high-draw headphones. But from a daily power drain perspective, I find that very hard to believe. Bluetooth transmitting is going to be orders of magnitude higher draw than corded earbuds. And when you're not actively listening, standby is still digging Bluetooth further in the hole.

No, overall, you'll be using more power (DAC vs encoding + decoding + DAC). It's just split across two devices you have to charge independently.

Evidence seems hard to come by on this subject, but a web search yields a lot of results along these lines:

https://www.quora.com/Which-uses-less-battery-for-a-car-audi...

It's hardly a scientific study, but it reinforces my prior belief that aux doesn't inherently require any electricity, while bluetooth is sending information over radio waves which of course has to use electricity.

I'm not sure about the difference when it comes to fancy, high-powered headphones, but my (anecdotal) experience with bluetooth vs. analog certainly supports the idea that bluetooth uses more power. I'd appreciate some citations if you have some other information about this subject.