Yes, the process exists, and the Church has developed a quite good process which the nuncios follow, consulting confidently with priests and even laypeople about possible candidates under Pontifical secrecy.
However, I think that during the last pontificate, and even since Vatican II, there was, in many cases, carelessness in selecting good candidates men who are truly men of God, firm and solid in doctrine, unshakable, genuinely pious, and who loved the tradition. This was lacking so much.
Therefore, we had episcopal sees, to a large extent, occupied by bishops who did not love the Catholic faith and tradition as they should, and who were influenced by worldly conventions and the spirit of this world, aiming more to please ideological slogans and the world.
The new pope should, I think, give precise instructions to the nuncios, indicating concrete qualities to look for in new bishops, and be very careful and attentive in approving the proposals he receives.
It is evident that from the bishops depends the life of the diocese, the life of the priests, and the people. A good shepherd must be completely rooted in the apostolic tradition, in the unchanging tradition of faith, liturgy, and morals of the entire Catholic Church.
Dear visitors of Gloria Dei and all who have already written or who will write a personal message to me. I am grateful for your attention, your kindness, for your spiritual support and especially for your sacrifices and prayers for me. God may reward you!