You must have missed the reminder to submit to the Holy infallible Father in Rome, or at least specifically to pray for him, or at least mention him (esp. among the 27 acquaintances in Romans 16), as Paul did in his epistles, and as befits a cardinal doctrine, since Paul was careful to always to declare "all counsel of God." (Acts 20:27)
You say you still not see the church looking to Peter as Rome teaches it did? Then read the Lord's critique and counsel to the 7 church in Asia, with its commendations and condemnations. For surely submission to Peter would be of primary commendation for the health churches, and commendation for those who were not, and part of the solution for such
Not there either you say? Then look how Peter describes himself in his epistles. Surely you can see that being "a servant," "an apostle," "an elder" is describing the exalted office in Rome to which all the churches looked to as their infallible head.
Such is not seen in any church epistles or letters you say? Then look how the entire church considered Peter's testimony and exhortation as being the definitive sentence on what should be done in Acts 15, rather than being the street-level leader among the 12 leaders, and first to use the keys to the kingdom, the gospel, (Col. 1:13) with no unique powers, and whose word did not settle the matter, but which the conclusive counsel of James did, confirmatory of Peter and Paul and Barnabas, after the latter added their complimentary testimony.
You do not see Peter as the singular supreme leader there? Then look how Paul describes Cephas (Peter) in Gal. 2. Surely being list second after James as one of 3 present who "seemed [appeared] to be somewhat" and that whatsoever they were as persons did not matter to Paul, and publicly reproving Peter for his duplicity is how Rome presents its pope.
You say you see the contrary, and not Peter as first of a line of exalted infallible heads in Rome is not there? Then look how the Holy Spirit is faithful to tell us of the successor to the apostle James who was martyred, (Acts 12:1,2) as He did for Judas (in order to maintain the foundational number. (Acts 1:15ff; cf. Rv. 21:14)
You still only Peter as the initial street-level leader among the 11 leaders, with no unique powers perpetuation? Then look how often Peter is mentioned as compared with everyone else, even if much of that is duplicate accounts. And how much God used him. You say that by that kind of criteria you could provide 51 proofs of a Pauline papacy ?
Well, if you cannot see how Rome can extrapolate support for what it declares as Truth out of what Scripture does not teach, then it illustrates why you need to submit your mind to Rome first, as if she was God, and then you can believe anything she want you to. Regardless of any cost to credibility.
Ain’t that the truth.