I can see why it might seem that way, but that's not how it works in the Church.
Rome and Constantinople are Pentrarchal Sees, as are Jerusalem and Anitoch - Alexandria is too but it's held by the Copts and largely outside the current discussion. Jerusalem is claimed by both East and West, Antioch has a an Orthodox See. Successful Union between East and West means reunification of Four out of the Five Pentrarchal Sees.
In this scenario the Patriarch of Moscow has two choices - refuse to recognise the Pope and create a new Schism between his Church and the centre of the Christian World or yield to the Pentrarchs. If the Russian people are not behind reunification then either choice is likely to fracture the Russian Church but on balance the Russian Patriarch would be better inside the new club than outside it. If Moscow forces a schism with Constantinople then those parts of the Russian Church that cleave to the Pentrarchs will default to Constantinople, leaving the remains of the Russian church to be gradually picked off. However, if the Russian Patriarch cleaves to Constantinople then he will be able to pick off the schismatic faction.
This is why Constantinople is essential and Moscow is now, Moscow can be cleaned up later if need be.
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