You need to re-read your history.
Three was no “Eastern Orthodox” form until the schism created by crowning Charlemagne “Holy Roman Emperor.” Until then the Emperor of the Easter Roman Empire was titular head of the Church. Authority was divided between multiple sites such as Constantinope, Antioch, Rome, etc.
By crowning Charlemagne emperor and claiming primacy, Rome split the Church.
I reread my post. I did not say WHEN the Eastern Orthodox form prevailed, merely that Rome did not succeed in suppressing it. The competition between Rome and Constantinople continued a number of centuries, as is pointed out in this link regarding this slow estrangement. Be sure to click the timeline chart below the explanation. I was surprised to discover that the “Dogmas of Immaculate Conception and of Papal Infallibility were later 1800s doctrines. Below the chart there is also a list of dated events.
http://saintignatiuschurch.org/timeline/
Rome was put as a tetrachy with two "Augustii" in charge of western and eastern halves and each had a "Caesar" under it as a successor, taking care of half of each half - so the Empire was basically divided into 4
The Western half was under continuous pressure from Germanic tribes (Vandals, Suebi, Franks, Marcomanni, Alleman, Goths etc) and Irani (Alans etc). By 400 AD these Germanics were practically rulers but kept the pretense of the Roman Augustus in Roman for show
Alaric changed this by sacking Rome, destroying the awe
Net - by 430 AD, the Augustus in Rome was deposed and never replaced.
The different Germanic princes didn't aim to succeed to the Augustii, not even the Merovingians.
By the 8th century, Byzantine (Rome - Eastern Rome) was under threat and there was only one power in the West that could provide any succour -- that was the Franks.
What better way to bring them into the Roman system by making the king as a Caesar/Augustus?
The Eastern Roman Emperors didn't accept this, but they had no military say -- oh and by the by, you do realise that many Eastern Roman/Byzantine Emperors came to the Imperatorship by the sword, right? and were of Arab, Armenian, Slavic, Albanian etc. blood?
When Charlemagne was made the Western Roman emperor -- Note, the term "Holy" Roman Empire only came about in the 13th century, Antioch, Jerusalem and Alexandria were under Moslem rule, so effectively split from both Constantinople and Rome -- and the Alexandrian and Antioch churchs had split earlier post Chalcedon
The Church was split primarily by politics mixed with nationalism (the Copts, Syriacs splitting as did the Assyrian Church of the East under the Sassanid Shahenshahs of Persia, then the Armenian Church)
By the time the schism occured in 1054, Westerners didn't speak Greek and Easterners didn't speak Latin -- they couldn't understand each other.
The schism, like the Protestant reformation must also be understood in terms of politics, ethnic rivalries, language and culture