The indirect, bluetooth microphones built into modern headphones sound utterly terrible.  The mane reason is all blueth microphones are limited to the 20 year old standard, 8khz sample rate & lots of compression.  

There's a rare example at 4:10 of all the most expensive headphone microphones.  Even without any singing or music, they all sound terrible or at least $400 instead of $500.

The 1st problem is the microphone cable is going to be a 2nd cable.  Maybe it could be farstened to the speaker cable.

Most boom microphones have a hole in the side of an earpiece.

Top of the line pilot headsets have an extension under the earpiece.