Perhaps because Paul’s point is that Christ is the head of the Church and that only Christ died for us. Our unity is in Christ. Yes Peter may have had primacy among the apostles but his point is that Christ is head over all.
We belong to Christ as those he died for, as co-heirs of the Kingdom, as children of God.
We belong to the Pope (or Peter when Paul wrote) only as sheep in the flock which he is called, by Christ, in Christ, and under Christ, to shepherd on earth, as both earthly leader and servant to all.
In addition it is probable that factions had developed in the Church of Corinth. The faction of “I belong to Cephas/Peter” was one of the factions, not out of obedience to Christ. The faction probably consisted mainly of Jewish Christians teaching that the Jewish law needed to be kept. Whether or not Peter had been to Corinth is debated, but they had heard of his character and surmised (in error) from what they knew that he taught the law needed to be kept.
So to call on the Corinthians at that time to follow Peter would have implied calling them to follow a Judaising legalistic faction rather than to follow Christ.
Even now, though the Pope is who he is, we can say we belong to Christ, not we belong to the Pope.
Of course, all of what I’ve just typed might be wrong - but it’s my stab at an answer.