Just not true. I fly all the time for work (4 flights a week), KLM eve announce that you can enable Bluetooth once flight safe mode is enabled and use Bluetooth headphones.
[0] https://www.faa.gov/news/press_releases/news_story.cfm?newsI...
[1] https://traveltips.usatoday.com/rules-using-bluetooth-airpla...
I mean I don’t think I can prove that literally every airline does allow Bluetooth headphones, but see previous comments where the FAA approved Bluetooth headphones for use in 2013, maybe you could provide a specific airline which does not allow Bluetooth headphones?