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We cling tightly to this tradition because it’s true, for starters, and because all Christians are commanded to do so by Paul in 1 Corinthians 11:2 and 2 Thessalonians 2:15. For biblical corroboration look at Acts 1:21-26, where you’ll see the apostles, immediately after Jesus’ Ascension, acting swiftly to replace the position left vacant by Judas’s suicide.
They prayed for guidance, asking God to show them which candidate was “chosen to take the place in this apostolic ministry from which Judas turned away.” After choosing Matthias they laid hands on him to confer apostolic authority.
Look at 1 Timothy 1:6 and 4:14, where Paul reminds Timothy that the office of bishop had been conferred on him through the laying on of hands. Notice in 1 Timothy 5:22 that Paul advises Timothy not to be hasty in handing on this authority to others. In Titus Paul describes the apostolic authority Titus had received and urges him to act decisively in this leadership role.
Lastly, please do better homework on early Christian writings. The testimony of the early Church is deafening in its unanimous (yes, unanimous) assertion of apostolic succession. Far from being discussed by only a few, scattered writers, the belief that the apostles handed on their authority to others was one of the most frequently and vociferously defended doctrines in the first centuries of Christianity.