That's actually my point.

I believe modern Bluetooth headphones are indistinguishable from equivalent non-Bluetooth headphones. If you can tell whether headphones are Bluetooth or not—the other components being equal—then you have particularly acute hearing. And if that's you, then you are probably a FLAC aficionado.

For what it's worth, I listen to MP3s on Bluetooth headphones and they sound great.

(Though to be clear, I've not actually researched the bit rate of Bluetooth, though I suspect it's high enough for 44 KHz stereo. To my ears, Bluetooth is indistinguishable from an analog 3.5mm connection.)

The quality has nothing to do with Bluetooth, it has everything to do with the digital-to-analog converter. A $25 headset is going to have the cheapest chip the manufacturer could find. Non-Bluetooth headsets don't process digital signals and don't have to do this conversion, it's up to the device you're listening on.

Okay.

Again, that's my point. Bluetooth has a undeserved/outdated bad reputation for adversely affecting audio. I contend that, all else being equal, I could not distinguish a modern Bluetooth wireless headphone from a wired headphone.

Yes, as you point out, they also need a DAC. So I will clarify my contention: all else being equal, I could not distinguish a Bluetooth wireless headphone from a wired USB headphone that uses the same DAC.

It's not all about the codecs. On my Sony MDR-1RBTs — which are admittedly a few years old at this point — you can hear the radio buzzing when there's nothing playing. I don't know if it's possible to design a pristine, noiseless set of Bluetooth headphones when there's just so little room in the earcups.