At the beginning of the 20th century the Pope appointed directly slightly more than 750 0f the worlds bishops, the remainder, the majority were appointed by emperors, kings or governments, or in some very few cases by local chapters of canons.
The practice of the first centuries was to elect bishops by popular acclamation of the laity and the clergy, local bishops ratified his election by participation in his consecration or at least by having his name inscribed on their diptychs. The Popes involvement was minimal and passive, but the bishop would pray for the Pope in the canon of the Mass, invoke its twenty-four saints, perhaps adding more according to long held local custom. Out of devotion, filial piety, he himself would either go on pilgrimage or send some of his clergy and leading laymen to the City of the Two Apostles, taking with them their bishop's portion of the Romefeoh or Peter's Pence. At the heart of this relationship the local bishop and the local Church shared the faith of the Bishop of Rome. The role of the Bishop was essentially to be the faithful bearer of tradition. For the most part heresies and aberrations of discipline were dealt with on a local level, first of all by the bishop himself or the metropolitan, or a local synod, brothers corrected brother. Only when this failed, or when there was serious doubt, or the need for an appeal, was there recourse to Rome.
It strikes me that the ideal way of electing a bishop today is by acclamation of the clergy and people. Though he should have an eye to the larger picture a bishop is primarily responsible for the people of his local Church, working in a paternal collaboration with his clergy for the salvation of the souls entrusted to him.
This is wonderful in theory of course but imagine the type of disaster that we would have today if the local church actually did elect its bishop. First of all the break down in catechises has meant that no-one is quite sure what exactly the Catholic or Christian faith is. The chaos that we see in some parts of the Church, for example, the toleration of the Archbishop Bathersby of Brisbane for twenty-four years of invalid baptisms and the open altar of Sr Mary's, the extraordinarily odd liturgies in the diocese of Linz, confusion over the divinity and uniqueness of Christ in much of India, the breakdown of marriage and teaching on sexuality in much of Europe, the diversity of understandings of theology and practice in the US, ranging from Fabian Bruskewitz to Roger, Cardinal Mahony and even in England we see the evident tensions between the doctrines of the Roman Church and what we see on the ground.