One use, as stated above, is that certified or registered is proof of mailing. This is what is needed if it doesn't arrive or the irs claims it was late. The green card is unnecessary.
Another use is when you tell the client to use priority and the package doesn't arrive or get processed correctly, the client has a valid argument that you should pay the penalties, which are your fault since you didn't follow clearly stated irs instructions on what constitutes proof of mailing.
There is no use of priority in this situation.