In the absence of internal evidence that the books were written by a specific author, the burden of proof is on someone who wants to claim a specific author.
This is an interesting matter for discussion: "Where lies the burden of proof?"
Let us say that, two-thousand years from now, in the year 4016, some copies of "Mere Christianity" are found, of the 500th printing, printed in the year AD 2400. While no earlier copies were extant, every copy found, whether from the 25th century or later, attributes the work to one C.S. Lewis.
Let us say, also, that there were found the works of some Christian writers from the 21st century, who had read the 5th printing, and who also referred to this book as a work of Lewis.
I think it safe to predict that the general consensus of literary scholars in the year 4,016, would take at face value the fact that "Mere Christianity" was authored by C.S. Lewis, even though no copies nearer than 350 years to his time had survived.
It is hard to imagine any reason that the churches of the 20th-through-the-25th centuries would have falsified the authorship of one of their most beloved and influential Christian books. Of course, there is that
possibility, but no
reason to suggest it.
If it was known that the man C.S. Lewis was a man qualified and motivated to write on Christian apologetics, this would give an even greater credibility to the "tradition" of Lewis' authorship.
Now comes a man with another theory. He believes that "Mere Christianity" was either written anonymously, or that it originally bore the name of a different author. He believes that the original author was either unknown to the original publishers of the first edition, or that they (or the publishers of later editions) knew the true author, but had reason to conceal his true identity from the church.
These would be interesting suggestions to explore, and worthy of inquiry, but if our conspiracy theorist had zero positive evidence to support his thesis, and zero negative evidence against the traditional view, and all he had was his subjective skepticism about the unanimous testimony of surviving documents, scholars might feel justified in looking askance at his assertions.
Of course, either the "traditional view" or the "conspiracy theory" might prove to be correct, but would there be any doubt as to which side bears the burden of proof?
Since the Gospels were written in the latter part of the first century, and were regarded by all known church authorities by, say, the late second century (e.g., Irenaeus and Tatian—AD 170), to be the works of Matthew, Mark, Luke and John, it would seem uncommonly bold to place the burden of proof upon the traditional view, in favor of a skeptical, 19th century conspiracy theory. If these men did not write these books, then we must assume one or more of the following (counterintuitive) things:
a) The Gospels fell into the hands of the first-century church without the church knowing the identities of those who handed them to them—perhaps appearing on the pulpit one night while everyone was asleep?;
b) The church was aware of the identities of the true authors, but had a vested interest in deceiving the next generation about their true origins—either out of embarrassment about the true authors or out of mere spite, wishing the future generations of Christians to live in deception concerning the origins of their founding documents (conspiracy theory—Big Time!);
c) The first-generation recipients of the original documents (which, unfortunately, did not bear the names of the authors upon them) knew the authorship, but failed to inform their children and the church leaders of the second generation, who also failed to inform the third generation, etc.—so that, less than a century after the books were written, the descendants of the apostolic communities were left to fabricate "traditional" authors for each book;
d) While these decades-removed custodians of the Gospels picked some, predictably, important characters to whom to attribute two of the Gospels (Matthew and John), they, shockingly, attributed the authorship of the two remaining documents to men of little standing and extreme obscurity in the early church (Mark is almost—though not quite—as obscure in scripture as is Tychicus; Luke is never named in scripture, except as a name in lists of Paul's companions, at the ends of a few letters).
It seems strange, if someone wished to fabricate authoritative authorships out of thin air, that men of stature would be passed over in favor of relatively unknown men. For example, Papias (one generation removed from the apostles) says that Mark wrote as Peter's interpreter, which seems to be Mark's principal claim to fame in the early church. If Mark really did not write the book bearing his name, why would the church, or Papias, attribute the book to Mark instead of Peter? If the early church wanted, falsely, to attach Peter's authority to the document, why not bypass the obscure, alleged middle-man?
Only a person prone to favor unlikely conspiracy theories (unfortunately, the description of a great number of biblical scholars) would suggest, without any evidence at all, that the early Christians either forgot, or deliberately deceived their children and grandchildren concerning, the true authorship of the Gospels.
Of course, if the church never actually knew the true authorship of these documents, there is no explanation as to why they so readily, and so early, accepted them as genuine, while rejecting a great number of apocryphal counterparts. My impression is that the church leaders were skeptical about accepting "apostolic" authority from unknown or unconvincing sources (Acts 9:26; Rev.2:2; 1 Thes.5:21). Yet, some time considerably earlier than that of Irenaeus, the church was not skeptical about any of these four books or their authors (
Against Heresies Bk. 3.11.8).
It would seem that a theorist speculating that the church either forgot, or deliberately misrepresented, the known authorship of their most sacred texts, within less than a century of their being penned, would certainly bear the burden of proof before any objective tribunal.