However,I would be very interested in understanding how you would plausibly explain the fact that the New Testament mentions Peter 198 times as compared to the 90 times all of the other Apostles together were mentioned.
Many of the references to Peter in scripture are in the context of conversations or directions or explanations or responsibilities given by Jesus (the complete Word of God) to Peter. References found in Acts seem to testify to Peter's authority and leadership as well as his supernatural gifts.
I think the humility Peter learned after his betrayal moved him far toward much more mature spirituality and God blessed him and his ministry accordingly.
The number of times Peter is mentioned is interesting. I've never heard of it as a criteria for Papal authority before.
Satan is mentioned a lot, too. I hope he's not in the running accordingly.