Bad audio quality with bluetooth on phones is mostly a myth. Todays smartphones only have cheap digital audio converters(DAC), so that you usually get higher quality music with a proper bluetooth codec like aptx.
Bluetooth poor audio quality is not a myth. The bandwidth is just not there for high quality audio. Even with aptx. That's why companies roll their own with BLE and the 2M phy. And even with that it's still flaky because it's wireless and can and will drop packets.
Yes, BLE audio is an improvement but those devices are still in the future. What you have currently, you're better off using your smartphone DAC.
Recently phones don't have DACs since they don't have headphone jacks. Well, they have them for the speakers and vibration but presumably you didn't mean that.
But their dongles' DACs are quite sufficient and are better than most of the audiophile DAC industry (which doesn't have the budget to actually make anything good).
I think codecs are where I have most of my remaining BT annoyances.
AptX is great (but there's also AptX HD, AptX.. is it variable? etc) - and exactly which AptX is supported varies by the Qualcomm chip in your phone and the device you're connecting it to.
Or you can go with Sony's LDAC. Works great on my Pixel, once I've turned on "quality" in the Sony App, then turned on the LDAC opton that gives in my bluetooth settings (and optionally can go into the dev menu each time I connect, to adjust the bitrate).
I do like bluetooth - but working out what features will work with which devices is a PITA. It always falls back to something functional, but fallback masks a lot of improvements that could be made. Although maybe that's the right approach. It works, and if you're somebody who likes to fiddle, you can.
But... Does the quality of a phone's DAC matter? I was under the impression that Bluetooth is digital audio. And the quality issue is with the bandwidth mostly or the headset DAC sucks.
Correct, the point was that the phones dac only matters when using the phones built in speaker, if you are using a blutooth audio device, then what matters for sound quality is the dac in the bluetooth device.
Yes, BLE audio is an improvement but those devices are still in the future. What you have currently, you're better off using your smartphone DAC.