Using iPhone mic with Bluetooth headphones

I want to use my ihpone microphone while on phone calls using my Bluetooth headphones. The headphones microphone quality is pretty bad and I want to use my phone instead so people can hear me. Before anyone says you can’t (as I saw on another question like this one) I’m currently doing it right now. When I go to unmute if my friend is screen sharing on face time, it gives me a drop down menu to choose microphone input from. It says “off” “iPhone mic (best quality)” and “Bluetooth headphones” (it’ll say whatever they’re paired as). I want there to be a way to do this normally, instead of only when someone is screen sharing on a FaceTime call. That’s the only place I’ve seen it be possible, but it IS possible and it should be a standard feature since a lot of Bluetooth headphones have terrible mics. I want to be able to have privacy in my call AND be heard by the person I’m calling. I’ve seen now that it’s possible, so let’s figure out a way to make it standard for all calls!