Potential Germs

With all the potential germs expelled when we cough, why do we use our hand? We've been taught to cover our mouth, but wouldn't it make sense to use a different part of the body? I've gotten now where I cough into my elbow - that way I am less likely to spread germs. How often do folks tough that part of your body in everyday contact? I am going to try and teach my child to do that. Maybe he'll influence some other kids to do it.