“You already conceded apostolic succession when Peter set the first election and the first group of disciples voted for Matthias.”
No I did not. It was not an “election.” No one voted. There was a casting of lots. It was choosing a twelfth Apostle to replace the traitor. There wasn’t succession.
“I pointed out that Peter had the keys to the kingdom of heaven and the power of binding and loosing so he had the authority to appoint other successors.”
Actually, all the Apostles were given this privelege. It had nothing to do with successors. That isn’t in the text.
“Before the LORD Jesus ascended to heaven he left Peter and his fellow apostles with all the authority they required. They had the authority to choose other men (Matthias is the example) upon which to bestow that authority, and to set the rules by which they would choose them (Matthias is the example).”
Casting lots was well established in the OT.
“The Scriptures need not list every man which they ordained to the ministry.”
Ordination is far different that Apostleship.
“There is a succession of men who have been ordained by the laying on of hands from the first apostles, generation to generation.”
Actually, historically it is broken, but the sanitized version of Romanism sweeps those details under the rug.
“Even if some were bad (Judas, for example) there were others who could be elected to replace them. One may think everything ended and changed with the deaths of Peter, Paul (who was not even counted with the Twelve and he was an Apostle) or John, but that is not written in Scripture either.”
What you’ve advocate isn’t written, commanded, demonstrated nor encouraged.
They had the authority for anything the holy catholic apostolic church required. All they had to do was ask in the Spirit. Many things that the LORD Jesus said and did are not "in the text." Many things the Apostles said and did are not "in the text." Sola Scriptura is not "in the text." What is "in the text" is that Peter, and the other Apostles, had the keys of the kingdom of heaven and the authority to bind and loose.