It’s part of the same reason why we still today hold collections for the Holy Land every Good Friday. Jerusalem is where Jesus was crucified and rose from the dead. Jerusalem is where the Church was consecrated by the Holy Spirit on Pentecost. As such, the Jerusalem Church is the “mother” diocese/patriarchy to ALL dioceses/patriarchies worldwide. Peter was the first bishop of Jerusalem, which he gave control over to St. James the Just, the so-called “brother” of Jesus when St. Peter moved on to Antioch and then to Rome.
The collection for Jerusalem for St. Paul, then, was a gift of thanksgiving to the Jerusalem Church - giving the mother of all churches the gratitude due to her. Today, of course, our Good Friday donations to the Holy Land are often the only income the parishes in the Holy Land receive, but it is also giving the Patriarchy of Jerusalem the gratitude due to her.