As I was seeking to prove whether the medal featured above of Pope Gregorivs III from the 8th century was really minted in the 8th century I stumbled upon this page with various pictures of Papal medals.
I happen to look through them quickly to satisfy my curiousity and I notice that all the Popes starting with in 1522 with Clement VII ending with in 1700 with Innocent XII happen to have beards, most of the time quite big ones in the 16th century. I can only assume that there was a trend in the 16th and 17th century to copy the greek philosophers and have beards to prove some sort of “greco-roman” philosophical statement?
Otherwise perhaps the influence was from unshaven monastic hermits and certain monks or friars?
Either way it is a nice fact of history that does bring their fashion in alliance with the Eastern Catholic/Orthodox Tradition of clerical/monastic facial hair.