Bob,
On modern standard gauge cars, they only go to one side.
No, actually it is because when kicking cars and working from one side, the knuckles open from the same end of the car, it prevents bypassed knuckles, drawbars and derailments from the same.
It doesn't always work, but it does in the majority of cases. The only modern broad gauge cars that I have seen with uncoupling rods on both sides are passenger cars and units (locomotives). The rest all have uncoupling rods that go to the left side of the car when viewing the end of the car straight on. Take a look for yourself.
Rick