It's not just a theory - it's the truth. There is historical evidence to back it up. Here is an example:
Clement's Letter to the Corinthians 42:4–5, 44:1–3 (A.D. 80):
"Through countryside and city [the apostles] preached, and they appointed their earliest converts, testing them by the Spirit, to be the bishops and deacons of future believers. Nor was this a novelty, for bishops and deacons had been written about a long time earlier. . . . Our apostles knew through our Lord Jesus Christ that there would be strife for the office of bishop. For this reason, therefore, having received perfect foreknowledge, they appointed those who have already been mentioned and afterwards added the further provision that, if they should die, other approved men should succeed to their ministry."
Clement was St. Paul's friend, and is mentioned in Philippians 4:3: “And I intreat thee also, true yokefellow, help those women which laboured with me in the gospel, with CLEMENT also, and with other my fellowlabourers, whose names are in the book of life.”
A pretty self serving position. Especially in light of the fact that no record exists of the Apostles appointing Bishops, or more importantly putting this in Scripture. The top down hierarchy developed later.
this is the full text of the portion of the letter you cite. there is nothing in the letter concerning apostolic succession. the close the letter comes to it is in the apostles appointing "firstfruits" to be leaders of the church. After their death it is the church that appoints just as the Didsche states. There is nothing in the letter stating only ordained men can appoint, in fact, it does not mention ordaination.
Chapter XLII.—The order of ministers in the Church.
The apostles have preached the Gospel to us from178178 Or, “by the command of.” the Lord Jesus Christ; Jesus Christ [has done so] from Or, “by the command of.” God. Christ therefore was sent forth by God, and the apostles by Christ. Both these appointments,Literally, “both things were done.” then, were made in an orderly way, according to the will of God. Having therefore received their orders, and being fully assured by the resurrection of our Lord Jesus Christ, and established Or, “confirmed by.” in the word of God, with full assurance of the Holy Ghost, they went forth proclaiming that the kingdom of God was at hand. And thus preaching through countries and cities, they appointed the first-fruits [of their labours], having first proved them by the Spirit,Or, “having tested them in spirit.” to be bishops and deacons of those who should afterwards believe. Nor was this any new thing, since indeed many ages before it was written concerning bishops and deacons. For thus saith the Scripture in a certain place, “I will appoint their bishops Or, “overseers.” in righteousness, and their deacons Or, “servants.” in faith.
Chapter XLIV.—The ordinances of the apostles, that there might be no contention respecting the priestly office.
Our apostles also knew, through our Lord Jesus Christ, and there would be strife on account of the office of the episcopate. For this reason, therefore, inasmuch as they had obtained a perfect fore-knowledge of this, they appointed those [ministers] already mentioned, and afterwards gave instructions, that when these should fall asleep, other approved men should succeed them in their ministry. We are of opinion, therefore, that those appointed by them, or afterwards by other eminent men, with the consent of the whole Church, and who have blamelessly served the flock of Christ in a humble, peaceable, and disinterested spirit, and have for a long time possessed the good opinion of all, cannot be justly dismissed from the ministry. For our sin will not be small, if we eject from the episcopate those who have blamelessly and holily fulfilled its duties. Blessed are those presbyters who, having finished their course before now, have obtained a fruitful and perfect departure [from this world]; for they have no fear lest any one deprive them of the place now appointed them. But we see that ye have removed some men of excellent behaviour from the ministry, which they fulfilled blamelessly and with honour