Wearing headsets of any sort in a business meeting is pretty unacceptable in most cases. There's a reason the one ear Bluetooth sets largely fell out of fashion. Sure, social conventions can change but they haven't so far.
But on a headset without a screen you can't quickly see and dismiss an email or text that comes in without pulling out your phone. Or you can't glance quickly at it to remember your next appointment. I found that the bit reduced friction actually made me much more likely to rely on my phone to manage my schedule.