> It's not like your brain can process each ear separately.

If you've ever seen a dance music DJ (Tomorrowland is streaming on Youtube right now!) - that's exactly what many of them do.

To DJ a continuous mix as is the norm for this style - generally you'll have headphones on, but only covering one ear. You'll listen to "currently playing" though your right ear, through the venue sound system (well, it's monitors). You'll also be listening to "up next", on the other record/cd/mp3 deck, through the headphones to your other ear. And you'll work the pitch slider, trim controls etc and hopefully produce a good mix!

Not everyone does it like this, some have the headphones permanently on and mix in stereo both tracks at both ears. Or split ears, headphones only - that is an option on the usual Pioneer mixers. But it's surely the most common mental image of a club DJ to have them holding their hand to their headphones on one ear only, I'm sure!