When using the "headset/hands-free" profile, which is required for bidirectional speaker/microphone usage, the quality of Bluetooth audio is absolutely terrible. All Bluetooth headphones that I could find don't have any other way to connect the microphone than via Bluetooth: although they come with an analog 3.5mm cord, it only has three rings, allowing for stereo audio and no microphone. Because enabling the microphone over Bluetooth makes both the audio input (to the headphones' speakers) and output (from the headphones' microphone) sound terrible, this is not ideal. Yet, I could not find any Bluetooth headphones that support any other method. Why is this?
Here's a few educated guesses.
Not much market demand. People that want a wireless headset will buy a wireless headset. Why put in a 1/8" audio input then? Because it's cheap and easy to do. If a 1/8" jack is so cheap then shouldn't a four connector TRRS jack that has the microphone output be cheap and easy too? Not really, because there's more than one way to wire that jack. https://en.wikipedia.org/wiki/Phone_connector_(audio)#TRRS_standards
If they wire it one way then half the market can't use the jack. If they include an adapter to swap the mic/gnd contacts then it's not so cheap and easy. Because a little adapter can be easily lost, assuming people read the instructions on when they are needed and when not, there would be a lot of returns and support calls. There's apparently circuits that can detect mic from gnd and therefore maintain global compatibility without the easily lost adapter but that adds to the cost.
There's two fixes for this. First is USB-C is making the 1/8" jack obsolete on most every portable device. There's only one way to wire USB-C for stereo audio out and mono mic in, assuming people follow the spec, and so no more regional differences on how headsets are wired. Second, Bluetooth is upgrading the connection bandwidth and digital audio codecs. The microphone quality will be better with new Bluetooth 5.2 devices. That's not helpful for your current phone but you were going to buy a new one next year anyway, right?
I'm still seeing far too many new Bluetooth headsets with micro-USB-B for charging and 1/8" jack for audio years after the spec to replace both with USB-C. I would have bought a USB-C headset last summer if I could have found one when I needed it. Maybe they will be more common when the headset I bought then dies. I checked the specs on the headset and it says it can use a TRRS cable to plug into a phone, it doesn't say if the microphone would work if wired though. I'm tempted to buy a cable to find out if it works.