Since the Pope celebrates Mass every day, and since many Eastern Catholic groups with married priests have the priests exercise continence every night when they’re going to be celebrating Mass the next day, the theoretical Pope’s theoretical wife wouldn’t be getting much action.
(If you know what I mean, and I know you do.)
This was one of the reasons why most of the devout early Christian bishops who were previously married, East and West, would usually become totally continent all the time when entering into the life of a bishop; and often, the wives would go off and become nuns so as not to be frustrated or provide a distraction.
The one Egyptian bishop who was once a student of Hypatia the mathematician, but who obviously wasn’t really a good neo-Platonist because he was too into his wife (instead of regarding all flesh as trash, blah blah blah), spent a lot of time refusing to become a priest or bishop because it would be burdensome to him and his wife in this way. And when he finally got forced to become a bishop (towns tended to elect you whether you wanted to bishop or not), he refused to send his wife away from the house (although he was apparently living with her like brother and sister), and it got to be a big controversy.
Currently in the West, the few married priests (and deacons) apparently don’t have to do this, but it does get brought up by canon law people and other interested parties (like folks from various places in the East). For the Pope as leader of many Eastern churches, it obviously would be a lot stronger consideration.