The Biblical record differs from your claims:
The qualifications of apostleship are listed in scripture. These include being a witness of the resurrection, being personally taught by Christ, and having confirming signs of apostleship.
2 Corinthians 12:12
Truly the signs of an apostle were accomplished among you with all perseverance, in signs and wonders and mighty deeds.
1 Corinthians 9:1
Am I not an apostle? Am I not free? Have I not seen Jesus Christ our Lord? Are you not my work in the Lord?
Paul opposed Peter because Peter was wrong. This is not an opinion. It is scripture.
Galatians 2:11
Now when Peter had come to Antioch, I withstood him to his face, because he was to be blamed;
Paul said Peter and the other apostles added nothing to him. Further, Paul claimed to be an apostle to the Gentiles to same degree Peter was to the Jewish believers.
Romans 11:13
For I speak to you Gentiles; inasmuch as I am an apostle to the Gentiles, I magnify my ministry.
Galatians 2:8
for He who worked effectively in Peter for the apostleship to the circumcised also worked effectively in me toward the Gentiles
Galatians 2:6
But from those who seemed to be something—whatever they were, it makes no difference to me; God shows personal favoritism to no man—for those who seemed to be something added nothing to me.
Peter did not specify that his authority would pass to someone he mentored but rather wrote his doctrine and historical record so they would remain after his departure (i.e. death).
2 Peter 1:15
Moreover I will be careful to ensure that you always have a reminder of these things after my decease.
Apostolic authority was necessarily embodied in people as the early church began, but that authority was preserved for the church in the form of writings by the apostles. We have all of the apostolic authority we need in scripture.
Revelation praises the testing of apostolic claims. Even in the early church their were many such false claims. When put to the test, many were found to be liars.
Revelation 2:2
I know your works, your labor, your patience, and that you cannot bear those who are evil. And you have tested those who say they are apostles and are not, and have found them liars.
Apostolic succession is false. It does not meet the requirements of apostleship. The Pope is NOT a witness to the resurrection of Christ. Those apostles who penned the New Testament were. Their record is one of eye witness testimony. This is an essential element of the gospel according to 1 Corinthians 15.
2 Corinthians 11:13
For such are false apostles, deceitful workers, transforming themselves into apostles of Christ.
1 Corinthians 15:1-5
Moreover, brethren, I declare to you the gospel which I preached to you, which also you received and in which you stand, by which also you are saved, if you hold fast that word which I preached to you—unless you believed in vain. For I delivered to you first of all that which I also received: that Christ died for our sins according to the Scriptures, and that He was buried, and that He rose again the third day according to the Scriptures, and that He was seen by Cephas, then by the twelve.
For many years the Catholic church opposed the people having scripture in their own language. This so-called “church” murdered those who dared to give people scriptures they could read for themselves. Having failed to prevent people from having the Bible, this so-called “church” has claimed to have more authority than the Bible, and that the Bible cannot be understood without the “church” to explain it.
I do not need to try to make sense of the words of a foreign-language speaking idolatrous apostle impersonator who speaks from both sides of his mouth, wears long robes and loves being called Rabbi and Father, when I can read the words of Peter, John, and Paul for myself. The Bible lets me hear from the apostles. It has all of the apostolic authority we need.