I'm sorry but this article reads like a fifth grade book report. Rather than provide any affirmative evidence of CoC beliefs, it claims any persecution as evidence and ignores evidence that refutes CoC teachings. It's basically a tautology - the logic goes like this: the CoC is the NT church, so any NT church is the CoC. This concept completely ignores any kind of evidence that would actually demonstrate a continuity of teaching, belief, practice.
For example - it says "Since the Roman Empire version of overly-organized and overly-formalized Christianity was not popularized until the mid-300s, every congregation in remote areas was on its own based on the Scriptures that would have been taken to them by the missionaries." The only reasonable response to something like this is - citation needed. And of course when we look in history we find the exact opposite - the episcopal structure of the church is there from the beginning.
Second example - the article assumes St Irenaeus is a witness to the CoC. But...St Irenaeus wasn't only a bishop, he taught the episcopacy in several places in his writings. So no autonomous congregations. He taught apostolic tradition and teaching being the vehicle by which the NT scripture and teaching were both delivered and protected. He actually says that the Church learned the gospel verbally, and only later received the texts. So no sola scriptura, no "we only preach the bible." He doesn't teach or quote from Philemon, James, 2 Peter, or 3 John, so his "bible" isn't even the same as yours. The CoC doesn't use creeds, correct? But St Irenaeus delivers several creedal statements in his writings. He also taught infant baptism. So, we can safely cross him from the list, I think. Definitely not a person who believed what the modern CoC believes.
Then they move on to St John Cassian. They make the laughable claim that St John Cassian "was condemned by Catholic church leaders around 428 because he opposed the teachings of Augustine about Rome being the city of God." I mean, this is almost not worth reading. St John Cassian was a monk from the East who went to Egypt, was ordained a deacon by St John Chrysostom in Constantinople, and later traveled to Rome at St John's request to appeal to Pope Innocent I over St John being exiled. He wrote at the request of Pope St Leo the Great. He was and is HUGELY influential, the author of the work that would become Pope Gregory's teaching on the Seven Deadly Sins. His writings were the basis for St Benedict's Rule, and he was never, never, never condemned. He is STILL recognized as a saint by both Rome and the East.
The article continues "John has been called a monk by many historians, a term loosely applied to many who were merely ministers of the gospel." I mean, come on man. This is silly. St John founded the Abbey of St Victor in Marseille. He wasn't "called" a monk, he was a monk, and basically brought the eastern monastic practices to the west. This kind of article is prattle for people who are essentially ignorant of history.
Your last paragraph is nothing more than an assumption or further argument from silence. But look, it's fine - the evidence doesn't exist because it didn't happen. It's not true. The CoC is 100% a product of the American Restoration movement. You know it, I know it.
