First of all, I'm not catholic and can't believe you don't know this after so many years here. Because I know catholic doctrine and agree with some of it does not make me catholic. I left that church about 40 years ago....after some study of both.
Vicar means a representative of a Bishop.
Vicar of Christ means a representative of Christ... any pastor/teacher/priest is a vicar if we can understand it that way.
The Pope does not take the place of Christ (except in confession) but only represents Him.
Of course the Pope could be the head of the institutional church.
Can ANY corporation function without a President or CEO? No.
Any denominational church has a hierarchy...it must.
I found the following which explains in detail:
The Protestant writer Andreas Helwig suggested that Vicarius Filii Dei was an expansion of the historical title Vicarius Christi, rather than an official title used by the Popes themselves. His interpretation did not become common until about the time of the French Revolution.[7] Some later Protestant figures claimed that Vicarius Filii Dei was an official title of the Pope, with some saying that this title appeared on the papal tiara and/or a mitre.
Catholic apologists answer the Protestant claims by noting that Vicarius Filii Dei has never been an official Papal title.[8] Catholics answer the claims that "Vicarius Filii Dei" is written on the Papal Tiara by stating that a simple inspection of the more than 20 papal tiaras still in existence—including those in use in 1866 during the reign of Pope Pius IX when Uriah Smith made his claim—shows that none have this inscription, nor is there any evidence that any of the earlier papal tiaras destroyed by invading French troops in 1798 had it.[8]
source: https://en.wikipedia.org/wiki/Vicarius_Filii_Dei
I don't understand the problem with calling a man that is responsible for the religious teachings and morality and spirituality of a community "father".
It just means teacher...just like Rabbi means teacher.
Jesus was called Rabbi out of respect for His knowledge.
In Mathew 23 He meant that we are to learn basically from the Holy Spirit that give us UNDERSTANDING more than teachings.
This would be what I agree with regarding Mathew 23:9:
Ellicott's Commentary for English Readers
(9) Call no man your father.—This also, under its Hebrew form of Abba, was one of the titles in which the scribes delighted. In its true use it embodied the thought that the relation of scholars and teachers was filial on the one side, paternal on the other; but precisely because it expressed so noble an idea was its merely conventional use full of danger. The history of the ecclesiastical titles of Christendom offers in this respect a singular parallel to that of the titles of Judaism. In Abbot (derived from Abba=Father), in Papa and Pope (which have risen from their application to every priest, till they culminate in the Pontifex summus of the Church of Home), in our “Father in God,” as applied to Bishops, we find examples of the use of like language, liable to the same abuse. It would, of course, be a slavish literalism to see in our Lord’s words an absolute prohibition of these and like words in ecclesiastical or civil life. What was meant was to warn men against so recognising, in any case, the fatherhood of men as to forget the Fatherhood of God. Even the teacher and apostle, who is a father to others, needs to remember that he is as a “little child” in the relation to God. (Comp. St. Paul’s claim in 1Corinthians 4:15.)
In 1 Corinthians 4:15 Paul calls hmself a father.
15For if you were to have countless tutors in Christ, yet you would not have many fathers, for in Christ Jesus I became your father through the gospel.
Verse 14 states we are as children. Making the circle complete...