Why does Rome not accept 8th Canon of 3rd Ecumenical Council, which gives full independence to the Church of Cyprus?

[SyroMalankara]

It is very important to make these things clear. If historical Rome failed to keep the Tradition of Synod style Church between equal Patriarchates with order of honor, and not the papacy, then Eastern Orthodox have a good argument that Rome broke the Tradition and canons of the Church and that Rome is actually schismatic, and not Eastern Orthodox.
This Canon 8 argument is very strong argument.

All of this would tell us then, that Papacy was built in defiance to the Church, and that Vatican I was the maximum of that defiance.

The argument is unclear because there was no uniform answer. At times, some areas were more Conciliar, at times other Patriarchs were more strong with rubber stamp Synods (see the Russian practices vs. the Greek or the Coptic Orthodox Patriarch vs. the Armenian Apostolic). At times, one would see the Conciliarity flourish and within less than 5 years the person of the Patriarch would be supreme. Rome has never fully been as Conciliar as the Eastern Orthodox - but then again, neither has the Oriental Orthodox Churches.