He deserves to be treated the way he does, mainly due to his un-Orthodox ways. Patriarchs CAN be deposed. And he has zero authority, other than over the Greek Church.
Be that as it may, the pope doesn’t want to be put in that position. The strength of the papacy is its right to choose, or at least ratify the choice of bishops. That went away in the Catholic states during the Reformation and has only been regained since the French Revolution. The basic claim is that true catholicity depends on union with Rome.