Although, in the old days, primates were really big men (to this day, in Anglican Canon Law, when a primate is in another diocese on Visitation, all jurisdiction is suspended including that of the diocesan bishop, and the Primate functions as Ordinary), they did not always get things their own way. One of my heroes, Bishop John de Grandisson of Exeter, a very grand and wealthy member of an important cosmopolitan family and a buddy of the reigning Sovereign Pontiff, was told that the Archbishop of Canterbury, with armed retinue, was approaching his see city on Visitation. He sent his own rather superior armed force out to give the Archbishop a bloody nose.
Ah, those were the days. One has visions of Vincent Nichols, in his delightful new role as the pope's right-hand man, coming to the end of the three-hour train journey from Paddington down to Plymouth ... the train is stopped by a large force of heavily armed Liberals ... shots are fired ... the invaders retire, carrying their wounded with them ... an exultant Mr Budd re-enters his see city in triumph to sit down to a victory banquet. Medieval church life had a solid reality and rootedness to it which we lack nowadays.
Primacy lost out to the tendency of the nineteenth century papacy to absorb other jurisdictions, and in the twentieth century many of the functions which might have seemed appropriate to primates drifted into the hands of Episcopal Conferences. It might be thought that a certain accountablity was lost when a personally discharged primacy was replaced by the impenetrable bureaucratic miasma of an episcopal conference. Primacy certainly existed in the first five centuries (v. the 'Apostolic Constitutions') as it does now both in Anglicanism and in the Eastern Churches (both 'uniate' and 'separated'). Its role in the future is, I believe, part of the dialogue taking place between the R C Church and Byzantine Orthodoxy.