I am not following your "by extension, their successors" argument. Jesus intended this power to be assignable by the Apostles? How do we know this? You need to develop this argument a little more robustly.
Fair enough.
I would start with the question, "Did Jesus train 12 Apostles during His earthly ministry and intend that to be the end if it? Or did He train 12 Apostles with the intent for it to be an ongoing ministry within the Church He created going forward?" I would argue the latter. The former doesn't make much sense unless Jesus was coming right back for the second coming as soon as the Last Apostle died, and that didn't happen.
Well, let's think about this.. Jesus reveals to us, for example in Matthew 18:15-18, that: “If your brother offends against you, go tell him his fault between you and him alone. If he hears you, you’ve gained your brother. If he doesn’t hear you, take one or two with you, that in the mouth of two or three witnesses every word may be established. If he will not even hear them, tell it to the—” What? “
The Church, and the one who fails to hear the
Church is to be as a heathen and a publican. For whatever you—” and by the way, that, in Greek, is plural; “whatever you,” plural, that is, the Church—”whatever [the Church] binds on earth is bound in heaven, and whatever [the Church] looses on earth is loosed in heaven.” There we have Jesus giving us—and I would argue—perennial instructions. In other words, Jesus doesn’t say here: “Now you can only do this until the death of the last apostle. After that, nope, it’s going to be Bible alone. You have to go to the New Testament and argue about it, and if you can’t agree, start your own separate church!” Right? No, Jesus gives us perennial instructions here.
Now, once you get there, what do we know about the Church? Well, the Church is described for us as hierarchical, right? In Ephesians 4:11, the scripture says “The Holy Spirit has placed in the Church Apostles, prophets, pastors, evangelists, and teachers.” So look, that Church that Jesus says you’re supposed to go to—and that Church will give you the definitive word, whether we’re talking about faith, morals, discipline, Jesus gives carte blanche authority here—he describes that Church for us, does Saint Paul, as hierarchical with particular gifts, and one of them being the Apostle.
Well, in Acts 1:20, we find an interesting text. Remember, Judas died. He committed suicide. And so when Peter is exercising the "keys of the kingdom" (Matt 16:19) to establish the Church—of course the Holy Spirit working through him—it’s interesting that he quotes a couple of Bible verses here: from Psalm 69 and Psalm 109 here in Acts 1:18-20, but especially verse 20, he says concerning Judas that his seat—remember, he was numbered with the apostles, the Scripture says, so yes, he was fully an Apostle—but he says in verse 20
“Let another man take his office.”
Now this becomes really important, because the Greek word there for “office” is
episkope.
Episkope means
bishopric. So now, when we’re specifically talking about the apostle in succession, you’ve got a replacement here for Judas that office, in succession, is called a bishopric. Well guess what? We have bishops in the Church, because 20, 25 years later, Paul writes about the office of bishop in 1 Timothy 3:1. And interestingly, in Ephesians 4:11, he doesn’t mention bishop, he only mentions apostle, prophet, pastor, evangelist, and teacher. Why didn’t he mention bishop? When he talks about bishop in 1 Timothy 3:1, why wouldn’t he say bishop here? Well, because the bishop takes the place of the Apostle, or succeeds the Apostle.
So the Apostle has a unique role inasmuch as the Apostle in the first century had to be an
eyewitness of Jesus. That’s something that the Apostle cannot communicate down through the centuries. So there’s a unique role and dignity given to the Apostles. But the
successors of the Apostles—that’s the key—are called
bishops. And this is why, down through the centuries, the Catholic Church has had bishops who are, in fact, successors of the Apostles. And a little tidbit of interesting information: every priest who is ordained a priest in the Catholic Church is ordained
by a bishop, and that bishop can trace his Apostolic Succession all the way back to one of the Apostles. The Church has kept meticulous records for two thousand years. Is that awesome or what? That is awesome. So, all this is all rooted in Sacred Scripture, correctly interpreted.