Now if it was so practical to have one leader of Apostles why would it not be practical to have leader of Bishops? There is certainly merit in this as it was Apostolic practice during when Church did not always have means to contact this leader… it would be sad that if now that it is possible this position wouldn’t exist anymore. You said how Apostles all knew Christ personally which is true. If those people needed leader, why don’t Bishops? It almost sounds like Bishops are more trustworthy than Apostles.
Fair and thought out response. You would almost have one convinced.
I will start out by saying we can not gloss over our differences of just how Peter was a leader. We can talk whether he was " appointed", or whether he was a leader quite naturally by disposition, and or a mixture of the two.
What also comes up is the idea of first amongst equals. Some say no such thing, but then others say no such things as two heads (Jesus and Peter), even though one is visible and one not. Scripture is quite clear that Christ is the head Shepherd. It is also quite clear He is ever present in and by not just the shepherd, but in every sheep. This is very unlike your reasonable explanation for needing a visible leader as in any worldly organization. The uniqueness of the church is His ever presence in every believer. Can you imagine if you were to look at every believer as His temple, even His monstrance.?
So yes we still need shepherding, but the invisible Head Shepherd is quite sufficient in and of itself. First amongst equals is not so far fetched then. What the early church did with councils and patriarchs is not so far fetched. We are not orphans without a visible head bishop.
I believe Jesus made no such office for Peter, though still a leader, and more certainly no office thereafter. As to those bishops that came afterwards, we trust God, even the Chief Shepherd, even the Paraclete, to provide a man for all seasons, a leader on any given situation in any time, as God sees fit, but working as amongst equals, not lording over like a worldly affair. ( and some popes were that man, but again, not exclusive to an office).
I really dont think the apostles needed the type of leader that the CC suggests. The Lord was strong in them and mighty in works, even unto to their martyrdom, save the beloved one John.