I think there's a confusion between classification and hierarchy. I would always use the plural when referring to Eastern and even more so Oriental Orthodox Churches. They are independent entities, though they have affinities to each other and can be grouped together based on what ecumenical councils they recognize.

In contrast, there is single Catholic Church, and just a century prior to Gregory's time it united all Christians in the Western Europe, apart from a few heretical / protestant movements here and there.