Rome the CITY did not, Rome the EMPIRE included both EAST AND WEST.
So what's your point?
The ROMAN Emporers Constantine and Theodosius I called the first two councils. The EASTERN Emporers (the empire was divided by that time) called the last five. The Church, prior to its split, universally accepted the primacy of the the Patriarch of Rome, followed in second place by the Patriarch of Constantinople...in a collegial fashion (i.e., the first and second among equals).
Each Patriarch was responsible for his own territory and doctrinal issues that impacted areas outside of each territory were decided by Ecumenical Councils. That, my FRiend, is the point.
If you want to scratch around digging for ants as to whether or not Constantine was a Serbian or whether or not Theodosius I was a Spaniard, feel free to do so. It's really not that important to me.