When we think of how Ethiopia was served by the Coptic Church, it was not by establishing the Coptic Church in Ethiopia, but by establishing the Ethiopian Church. Such a thing as the Coptic Church in Ethiopia would have been a contradiction in terms, since the Coptic Church is the Church in Egypt...
The Armenians had parishes serving their people in other territories, such as Rome, from the very early centuries. But I don't think it was as an independent Church with its own hierarchy. It was parishes to serve that need, with the cooperation of the Armenians sending priests to serve and the local bishop's approval.
Fast forward to today, and things in North America look quite different than (my limited understanding of) the past.
The Church Coptic Church was the first large presence here. But they did not set up an American Orthodox Church, or a Canadian Orthodoxy Church as they previously set up the Ethiopian Orthodox Church. They set up the Coptic Orthodox Church in Canada, which is a contradiction in terms. This has been a result of, and has resulted in, much confusion. I read a book by one Coptic priest that thanked God that in the past decades the Coptic Church has gone from being a national Church to a Catholic Church!
This is of course because of the unique situation of large immigration meaning that the Churches here are full of Egyptians, and few Americans/Canadians. Much different than a few Copts being sent to serve the Ethiopians. However, this is problematic, because it is inward looking, and does not meet the idea of engaging the surrounding community and preaching the Gospel. It is even more problematic since the children of Egyptians here eventually become Canadians, and not Egyptians! They marry Canadians, and since there is no Canadian Orthodox Church, many of them end up leaving the Coptic Orthodox Church, which is too foreign for their spouses.
Now, there are many other Oriental Orthodox Churches here as well. Instead of integrating into the existing hierarchy of the Canadian Orthodox Church, which was never established, they set up their own shops, independently of the existing Coptic Orthodox presence. Different Oriental Churches in the same towns that don't even realize they're in communion with each other for the most part. Yes, an Ethiopian bishop is received in a Coptic Church as their own bishop. But the Churches are governed as independent, separate Churches. Instead of one local synod, made up of bishops from all the different ethnic groups, working together to serve the needs of Canadian, Coptic, Ethiopian, Armenian, etc., parishes, we have separate groups, duplicating resources, and acting as if we were separate Churches or denominations, each ruled by the synod of their home country. I don't think there is any precedent for this in Church history.
I think there are agreements or understandings that the Coptic Church should consult her sister Churches when establishing diocese in North America. But so far they have just been established without cooperation or resistance.