If having wide bars helps with climbing, why are road bike bars so narrow? And aerobars on tribikes are super narrow...if this were such an issue, wouldn't breathing trump aerodynamics? And why don't people run with their elbows out?

Along with leverage, wide bars also help with power. Next time you're at a gym, see how much you can bench with your hands close together, and then see how much you can bench with a wider grip. Same principle applies to pumping terrain.