Is not the entire reason for this debate that the Orthodox and Catholics have differing understandings of what the "first see" implies and why that is important. This makes no sense to bring up.
Also, if the Church of Rome accepts the Council of Chaledon (particularly canon 28) as Ecumenical, then the fact that Rome was the "imperial city" does certainly factor into her primacy. I don't see how this would damage the Catholic position either.
Do you expect a different answer than a Western Rite Catholic? How is a group of Catholics holding to Catholicism or a group of Orthodox holding to Orthodoxy a premise worth arguing from?