Paul is calling the Corinthians to holiness, so that they may be bold enough to return the greeting of the saints. For they are greeted by the saints with the intention that they should imitate them.
And having said, "Salute one another with an holy kiss," he added, "All the saints salute you." By this also giving them good hopes. He has added this in the place of the kiss, knitting them together by the salutation, for the words also proceed from the same mouth from which the kiss. Seest thou how he brings them all together, both those who are widely separated in the body and those who are near, these by the kiss and those by the written message?
[AD 384] Ambrosiaster on 2 Corinthians 13:13