Brother:
Please explain what you mean. What comes to mind when I read your post, is that Pope Gregory the Great specifically rejected the title, "Universal"........
Universal primacy is the recognition of Ecumenical Councils of the Bishop of Rome as primus, i.e. "first" in the whole Church. The stumbling block is (and was even then) what that entails and how does that translate into jurisdictional primacy.
The Church was organized synodally, with Ecumenical Councils being the proclamations of the Church, infallible, as the Church is, and binding. The East is still organized that way, but the West is not.
The Pope recognizes that. There is even talk of "pre Schism papacy." At any rate, this should not be understood as willingness on the Latin side to sell out what they earnestly believe any more than assuming that we will betray our convictions.
We must define a mutually-acceptable Petrine Ministry that will not be stifling, overwhelming or chauvinistic, imposing or desiring to lord over other Patriarchs, and yet to be the unavoidable and essential element in all Church decisions.