Being able to breathe to either side can be useful in both open water and pool swimming, and developing the skill can also correct some stroke flaws. Two Feel For the Water blog entries recently addressed this issue.
The first blog detailed how a professional triathlete was actually less efficient when breathing to his “comfortable” side. The article explains how a stroke flaw was first revealed by comparing swimming speeds while breathing to the strong and weak side.
The other post describes a drill to help develop your weak side breathing by using a single paddle and fins, as shown in the figure. (If you are a moderately strong kicker then the fins are really optional.) I would add a suggestion that you do some freestyle repeats where you only breathe to one side during an entire length of the pool, switching sides as you go (eg, sets of 100s where you breathe to the right on the odd 25s and breathe to the left on the evens).
Besides any improvements in mechanics, the ability to comfortably breathe to either side would seem to be important in OW swims as a way to avoid (for example) the sun or waves on one side, or to keep your eye on your competitors or the course buoys. Give it a try!