Clearly such a candidate would be preferable while available. This does not, however, imply that their office would cease once these no longer existed. By your reasoning Paul himself would not qualify as an apostle.
Elders are a Church office. They were appointed in each church. We still have elders today.
Not true, they were appointed for each church.
For this reason I left you in Crete so that you might set right what remains to be done and appoint presbyters in every town, as I directed you. (Titus 1:5)The presbyters were not appointed by the local congregation but by one who had already been invested with the apostolic authority to do so.
“Clearly such a candidate would be preferable while available.”
Not only preferable, but specified. No other path to replacing Apostles is given in Holy Writ.
“This does not, however, imply that their office would cease once these no longer existed.”
Sure it does. It is an argument from silence in the Scriptures, as no other method is given. No criteria is given, as it is with elders and deacons. Further, the Apostles & Prophets are called the foundation of the Church.
“...then you are no longer strangers and aliens, but you are fellow citizens with the saints, and are of God’s household, having been built on the foundation of the apostles and prophets, Christ Jesus Himself being the corner stone, in whom the whole building, being fitted together, is growing into a holy temple in the Lord”
“By your reasoning Paul himself would not qualify as an apostle.”
Here you’ve discovered the second revealed way of choosing an Apostle - The Meet Christ on the Road to Damascus and Be Struck Blind Method. Further, since Paul was not with the Apostles from the beginning, so the glorified Christ caught him up into the heavenlies to personally instruct him and reveal His Gospel of Grace along with things that were unspeakable.
That said, unless God intervenes on earth, Paul is gone to glory and there are not others being snatched up into heaven or being struck blind.
“Not true, they were appointed for each church.”
I refer you to the Epistles where instructions are given on how to choose elders.
“The presbyters were not appointed by the local congregation but by one who had already been invested with the apostolic authority to do so. “
At times yes. It is not required in Scripture.