Keys represent authority. By virtue of being given more work and being used to write more scripture, Paul exercised more authority. He also withstood Peter to his face over poor doctrinal practice. Did Paul overstep his authority?
In Matthew 28, was Peter singled out to receive authority that that the other Apostles didn't receive? Why not?
Does Peter speak with more authority than Paul?
Does Paul say what Peter is writing things difficult to understand?
Again, Peter was given a great position of authority in the early church. But his authority came from Jesus. And nowhere does the Bible assert that he had the authority to choose a successor, or any else for that matter. According to Ephesians 4, it is God who gives some to be Apostles, prophets, etc.
More work never means more authority, that's ridiculous. Paul did rebuke Peter, and Peter was humble, not like the current pope, who thinks he is infallible. I never claimed Peter was infallible either, so no Paul did not overstep.
In Mathew 28 all disciples had authority to go out and make other disciples, but Peter was still chief, as evident in the verse I provided. Peter was generally first to speak and to punish and excommunicate people, so yes, he spoke with authority.
I don't see what being difficult to understand has anything to do with having authority.
Mathew 16:19 in light of Isiah 22 is what proves the line of succession - a king (Jesus) gave keys to the kingdom (heaven) to his chief stewart (Peter) that has the power to open and shut (bind and loose) and is passed down to his posterity (bishops).