The Importance of dripping coral is to remove unwanted and dangerous pests. Keep in mind where it truly comes from so it is no fun to spend money just to discover a few days later that some hitchhikers came along the way. These include acropora-eating flatworms or even soft coral eating-nudibranches that are eating away your new piece. Not only that but it protects your existing corals in the case you had them spread throughout your tank eating the others away.
Along with that it refreshes and helps heal new coral after the stress of fragging and shipping by helping sanitize irritation or wounds the coral may have suffered – helping to reduce the chance of infection while your new coral acclimates to your tank.