If Peter, Linus, Anacletus, Clement, etc. etc. had lived from the 21st century, maybe they would have done just that - or been satisfied with a handshake. We can only speculate.
But you need to consider traditions such as these in their historical contexts and not impose 21st century sensibilities on the common practices of the faithful from 33 A.D. through the early and middle ages to the modern era.
The Popes, bishops and priests all held authority in the Church structure. Signet rings historically symbolized the authority of the offices held by the persons. Kissing the signet ring of a king, queen, prince, bishop or pope was a courtesy as common as a courtly bow or salute. The custom simply passed out of style in the secular realm over the centuries, but remained a part of church tradition. The action holds no theological importance. It is merely a polite form of acknowledging the position held by the particular person.
Peace,
-Robert