You're looking at it the wrong way. Not why do we have beards, but why did we lose all our other hair?
Cats don't have beards, because cats have fur.
Because it's harder to shed heat when you're covered in fur.
Saw the docu Becoming Human today and that was the main theory they purported. Didn't catch why we managed to keep things like pubic hair (which always confused me), head hair made sense in colder climes, and thick hair growth on the body is connected to testosterone in humans (unrelated to the docu).
From my understanding its body temperature regulation and before human lost the ability to do phomena some of that to.
I'm not an expert on this by any means, but here's a side-note:
Humans have been incredibly good hunters because they hunted through endurance hunting. They simply could chase animals for so long that the animal would become exhausted while the human could keep going. We managed that through temperature regulation--we sweated and we had very little body hair. Without that fur, we would not overheat and dehydrate and all that bad stuff.
As far as pubic hair goes, I have no idea for females, but I speculate (only speculate) that pubic hair might have stayed on men, potentially and partially, to help keep the epididymis warm so that sperm didn't die. I learned in high school health classes that sperm needs a remarkably regulated temperature to stay alive and so I'm guessing some sort of link from that to pubic hair.