If the role of apostle was to be handed on, then one would have thought that such an office would have been bestowed upon Polycarp, who was a disciple of the last living apostle, John. Polycarp never wrote that either he nor any other of John's disciples was ordained an apostle. There are no historical texts that reveal that any other apostle ordained any of their disciples to that office either,
There is evidence there were other apostles ordained in the NT church--other than the original twelve:
Acts 13:1-3---King James Version
1 Now there were in the church that was at Antioch certain prophets and teachers; as Barnabas, and Simeon that was called Niger, and Lucius of Cyrene, and Manaen, which had been brought up with Herod the tetrarch, and Saul.
2 As they ministered to the Lord, and fasted, the Holy Ghost said,
Separate me Barnabas and Saul for the work whereunto I have called them.
3 And when they had fasted and prayed, and laid their hands on them, they sent them away.
Those two then appear here as apostles, for the first time:
Acts 14:14---King James Version
14 Which when
the apostles, Barnabas and Paul, heard of, they rent their clothes, and ran in among the people, crying out,
but there is ample evidence that many were ordained to be bishops, and there is evidence that the primitive church had priests, but the Aaronic or Melchezidek priesthoods were never mentioned as being conferred.
While I would agree there is very little mentioned about the priesthood within the Biblical NT--how could one be a priest, unless it was conferred upon him--and by one who had authority to do so?
There are also records that the apostle John "fell asleep" in Ephesus and was interred there, contrary to mormon teachings. What we know about the mormon priesthoods is somewhat sketchy in that the "experiences" were by 'second sight' encounters or visions. I'm not saying that something like that could never happen; however, I believe hat if those offices were to be passed on continuously until the return of Jesus, then records would have been kept for such important events.
"In May 1829, Joseph Smith and Oliver Cowdery went into the woods along the banks of the Susquehanna River to pray concerning baptism. In response to their supplications, a messenger appeared to them, told them he was John the Baptist and laid his hands on the men. He then said:
"Upon you my fellow servants, in the name of Messiah, I confer the Priesthood of Aaron, which holds the keys of the ministering of angels, and of the gospel of repentance, and of baptism by immersion for the remission of sins; and this shall never be taken again from the earth until the sons of Levi do offer again an offering unto the Lord in righteousness." (Doctrine and Covenants 13.)"
Again--more heavenly appearances--which events are replete in The Church of Jesus Christ of Latter-day Saints.