But the Egyptians didn't speak Coptic, they spoke Greek.
And the Antiochians didn't speak Aramaic they spoke Greek.
The local languages were used by those who were either outside the zone of civilisation or of a lower class.
St Severus preached in Greek, and in his own lifetime his homilies were translated into Syriac for those beyond the city of Antioch. But as far as I remember from the tables in Price's Acts of Constantinople, it was only in the 5th century that Syriac began to be used for literate purposes.
Likewise St Shenouda was among the first literate authors in Coptic.
Everyone spoke Greek. There were Greeks in Italy. Even the Irish aspired to some Greek knowledge.
Origin meant nothing in the ancient world. There were no nation states such as we have now. My dear St Theodore of Canterbury was Archbishop of Canterbury in the 7th century, and is buried just 20 miles from where I am sitting but he was a Syrian.
Why do you think it odd that there was such movement of people? We can surely think of many saints who moved around. St Peter the Iberian was from Georgia, lived in Constantinople, then became a monastic founder in Palestine.
Even in our own times we have had a Polish and now a German Pope. If the Church is universal then this happens. The Church of Antioch in the time of St Severus was not the Anti-Chalcedonian Patriarchate of Antioch, it was just the Patriarchate of Antioch.
Think also of how the Emperors themselves were from a wide variety of places of origin. There was nothing unusual in this. People were part of the Empire, and attached to their towns and cities. Even in Britain after the people were left to fend for themselves they considered themselves Roman for centuries.