Your Bluetooth headphones have their own batteries. They also have terrible sound quality compared to equivalently priced wired IEMs because powering multiple drivers/speakers per ear for maximum quality takes more power.

The dac is running off the batteries in your Bluetooth headphones, so that's a pretty natural outcome.

And the power amp which probably consumes more power than the DAC.

The size of batteries in two piece earbuds is miniscule and would not make a difference in phone runtime.

...and people still want to manually disable bluetooth on their phone "because it eats up their battery".

Dude. You posting that message to FB took more power than your idling bluetooth will spend all week :D

I turn it off because historically it's just less secure WiFi, and, bonus, junk to use more often than not.