Interesting and good point about Luke being a fellow-laborer/disciple of Paul as well as among Jesus disciples. Never thought about that but that gave Luke a deep and wide perspective about the amazing and surprising way God moved in the book of Acts, which of all the New Testament books, does not have an “Amen”. The works in Acts continue through today among those willing to surrender to Him by grace.
As far as “The Apostolic age passed with the death of Beloved John...” that may be true, but I certainly know of no scriptural basis for that assertion. Again, the Book of Acts never concludes with an “Amen” and the works therein are meant to continue until he returns, unlike the “traditions of man” that are taught in so many churches.
Going back to what the Scripture says and what it does not say, the only men commissioned as apostles by The Christ were The Eleven and Paul. They were authorized to recruit, baptize and teach disciples who were then, when trained, authorized to make more disciples, down through the ages. What they were not authorized to do was to make more apostles. That was solely the prerogative of The Lord Jesus Christ, Who was given all authority in heaven and on earth. He did not delegate the whole spectrum of that authority to His Disciple-Apostles, did he?
They were also prophets, eye-witnesses of the Only-Begotten-in-the-Flesh Son of The God and hearers of what He said. They were gifts to the churches which they planted (Ephesians 4:8, 11). On Beloved John's death, the last of the Apostles alive, the progressive Special Revelation ceased, and the canon of Scripture was closed. But we still have disciples being recruited and invested with the indwelling Holy Spirit through faith alone in Christ alone, with men of God being called--evangelists, pastors, and teachers, to lead their successors into spiritual maturity under the guidance of the Holy Comforter. The Apostles and prophets have done their job: completing the supply of the generative seed The Word, and broadcasting it onto good soil that it may multiply and prevail over the tares of Hell and damnation.
I think we need more sowers.