Approaching girls in public has high social consequences. I've read enough reddit [0][1][2] or seen enough news articles about people banned from businesses because a guy was seen as creepy.
Men need to learn what is ok and not ok when communicating with women. This is already an challenge because what is ok with one woman is not ok with another. Add in the shifting society view of what is appropriate turns it into an impossible task.
It just seems safer to do nothing and wait for the girl to make the first move.