Yes! Myt DD's BFF does competitive rock climbing. Her gym is as big as DD's gym, but covered in simulated rock faces. I don't know much about the sport, but I can tell you that competitions are usually pretty far away. Her mom is always telling me about trips they have to take to neighboring states here in New England. I guess there aren't as many rock climbing teams as there are gym teams, so to compete you end up driving pretty far.
Along with all her safety ropes, she wears a belt with a bag of chalk while she's climbing. AFAIK, it's the same chalk our gymmies use. She also gets these super cool little shoes that help her stick to the rocks.
You asked if it's safer? I don't know of any reports that compare competitive rock climbing to gymnastics, but I can't even begin to imagine that it isn't safer. I've never ever heard of any kid getting hurt doing it. There is no actual "rock" climbing in competitive rock climbing; it's all very controlled and simulated. I think "dangerous" rock climbing is done by those who are doing it as an extreme sport (like free climbing) and not competing in a rock climbing gym.