I ride with headphones routinely in all kinds of conditions. Contrary to what the party line appears to be, heavy traffic seems to be the safest place for headphones that I have experienced.
I actually don't wear headphones out in the country anymore. Out there, there is rarely a shoulder, and you can hear cars coming a mile away. (literally sometimes) MUPs I try to avoid too, since there is some verbal communication that goes on between the users of the path. People passing me isn't a problem, since I ride on the right side, except when passing, in which case I have to do a visual check anyway. In heavy traffic though, it's almost impossible to get any useful information from sound. If I'm surrounded by dozens of cars, I'm not going to hear that a car is about to cut me off. The sound of cars can alert us that they are there, but in heavy traffic, we already know that there are cars everywhere. I guess if you like listening to the drone of engine noise go ahead, but I'll take music.
FWIW I've never been involved in a collision that was related to the headphones.
The most serious one I was in was a low speed collision when someone illegally (against a posted sign) right turned on red in to my path. Actually, I only hit them after they saw me and slammed on the brakes, and then it was too late. I saw them start moving and was planning to duck behind them, but when they abruptly stopped, I had nowhere to go.
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Bring the pain.