No I wear both. Just dont set the music too loud, just enough to hear the music and it don't overpower everything. Vehicles are usually very loud so just make sure your music isn't louder than them.

But I still can perceive my surroundings because I regularly turn my head around left and right to check my back while riding on the road. In top of that I occasionally wear a mirror on my right wrist too. Both are habits from me riding motorcycles

Only useful if one has the habit of regularly checking. Some will deem it troublesome,because it takes your eyes off the road in front of you.

I know many cyclist only pedal pedal pedal and look forward without giving much thought about their back. Not a good practise but hey who am I to complain?

Be responsible for own safety lor.