There are actually secular “overtones” that have been colored with the recognition of Peter’s Authority to “bind and loose”. How many jokes that we know of talk about someone going to heaven where they are greeted by Peter at the gates.
I believe for the Protestant interpretations that I have heard to make sense, one must assume that the entire population of the earth at the time was the Apostles - just the twelve and no one else. Or maybe that these were the only followers of Christ. We know this not to be the case because of the loaves and fishes story for example, but to make it make sense the way they see it, you have to take this view.
They claim that the power given to the Apostles and more specifically to Peter was given to ALL Christians. It was not. If it was meant for ALL, it would have been given to ALL. As it was, it was given to ONE. The one who was the first to have the revelation from God that Jesus was The Messiah.
You also frequently hear grammatical gymnastics being played over the phrasing and wording of the verses you mention. Things like “on this rock” was not referring to Peter (who had just been named “rock” by Jesus) but to the revelation that Peter had, etc. which of course violates antecedent reference and some very common sense of the translations and the original script. Then, you also have the fact that NO ONE had this interpretation of these Scriptures until the 16th century, where the Renaissance (sp) Man finally had the brains and sophistication to “reason” away 1,500 years of understanding, and proclaim that all previous understandings of this simple text were in error.
I have personally witnessed some very desperate attempts to rationlize any meaning other than the meaning that is there - that Peter is the rock and Peter was given the keys and the power to bind and loose. The source of the desperation is that the truth un-does 480 years of “reformed” (“deformed”) thought regarding Faith and worship.
And now, that desperation is continued to try to lure people from the truth.