It's also injury prevention. It's good to train a variety of skills on both right and left, walkovers are also important to train on both sides. Otherwise the muscles develop unevenly, the stsses are always out on the same side and there is an increased risk of injury. Onvbviously bigger skills can't be done on both sides, so if basics are least being evenly distributed it can really help.
I think it makes them think about the technique more when they have to try it on their not so good side. I have girls in my tumbling classes try "other leg" cartwheels if they have mastered their dominant side.