So? Why is this a problem? Mt. Athos is in Greece and the article refers to "Greek-speaking monks" not ethnic Greeks. One can always learn the language.
1) Technically, Mt. Athos is neither in the Hellenic Republic nor the Church of Greece.
2) Hellenization ignores the difference between "Greek-speaking" and "ethnic Greek," insisting on the former in producing the latter.
3) Mt. Athos derives its standing as the giant in the Orthodox world from the various nationalities having monasteries there, which in turn had a profound effect back home (e.g. the Hilandar monastery and the Churches of Serbia and of Bulgaria).
4) If the Phanariots think this is going to extend their influence, they will just diminish the standing of Mt. Athos in the Orthodox world, to just another stronghold of Omogeneia, ignored by the "barbaroi" who will develop their already established centers back home.
5) and yet another area of Orthodox solidarity will bite the dust.