I can try, but I am a little short of time at present so this post will be brief.
But it really needs to be a book.
In the early Patristic age the argument was made that bishops could trace their foundations to the work of certain Apostles, thus St Irenaeus of Lyons (for one famous example) could point out that the church of Rome and the churches of Asia had this type of origin over and against some ‘other’. That ‘other’ was any of numerous heretical groups, mainly gnostic in one form or another.
Why was this important? Was it some kind of institutional seal of approval? Well yes, but the reason was the
teaching. It was important to prove that the teaching of these bishops in his day was the same as the teaching of the Apostles in their day! What they needed and wanted was consistency.
Otherwise, there were probably a lot heresiarchs around the late Roman world who could claim that they had Apostolic succession too. The difference was the stability of their teaching, and the indisputable fact that other such centers of Apostolic succession agreed with them going back to the beginning, they all agreed with one another.
They weren’t arguing that they all had Apostolic succession and that was all they needed. What they were arguing was that their teaching was trustworthy. It was authentic teaching, and the Apostolic succession was one way to tell, like a sign of authenticity.
Christian early history has many accounts of bishops visiting a church in some remote place and discovering heretical books there. That was their job, find out that kind of thing and make corrections (in those days it wasn’t as easy as looking at the bookshelf and reading the bindings, they pulled these scrolls and codices out and read them).
Another element of this was that it was ‘churches’ the Apostles founded, in other words communities and clergy, a complete package. It wasn’t like the Apostles were just placing chairs in temples and saying “the man that sits here is my guy, my job is done”. They were communities of Christians, responsible for one another, worshiping together and choosing their bishops when the predecessor passed on. The ‘office’ was passing through the community to a man, then through the community to the next man. That was the ordinary means of succession.
Bishops were not supposed to move around from See to See either, they were supposed to stay put until the breath left them. This is in stark contrast to the role of an Apostle (one who is sent).
The reason it required three bishops in the early church to consecrate another bishop was more a quality check. It was a control mechanism.
What we have today has stood all that on it’s head. We are saying that if the person had laying on of the hands, he is a bishop no matter what he believes, regardless of character, whether he even has a flock (or community) to serve. And then we compound this and say now he can make another, and that third one can make another etc.
And we are supposed to allow people to partake because their bishop has ‘Apostolic succession’? If the ‘bishop’ is no good what can we really say about the flock? How can we know since that ‘bishop’ is on the outside looking in?
Someone we never met and do not know can make bishops out of atheists and people of perverse dispositions who would presumably have ‘Apostolic succession’. This is why there are vagantes, this is why we are having this discussion right now about ‘who has it’ and ‘who doesn’t’, as if that subject can be separated from the teaching and the shepherding.
We are looking at this as if the laying on of hands is magical instead of sacramental.