If the canon had been decided by a dozen good old boys in a basement with a case of 'shine and a stack of scrolls, deciding what should be "promoted" to canon and what shouldn't, then the question of the authority would ride on Paul's having written them and saying so, and a bunch of drunks.
FF Bruce ("The Scrolls and the Parchments") and Neil Lightfoot ("How We Got the Bible") among others, argue an entirely different scenario took place. According to them, what was canon of the New Testament, FOR THE MOST PART, was considered self-evident. They were written within the 1st century AD, and all carried the feel of Scripture and the quality of same. (I'm paraphrasing heavily for brevity's sake.) What didn't make it, FOR THE MOST PART, was agreed to have been clearly of a different caliber. There were books written several centuries later, and most pushed some esoteric or Gnostic POV that felt like it didn't match the others. As for books like "the Infancy Gospel of Thomas", that was written as a fanfic and was accepted as such at the time- considered good for entertainment but hardly Scripture. When just grabbing all old documents together that didn't make it and calling them some sort of "Lost books" or "forgotten books", that's a lot like grabbing the contents of my Bible case (with any songs, poems, short stories, etc) and claiming they're of equal authority as the Bible that's in the case because it's in the same case. That was possible then because they didn't have leatherbound Bibles as a single book- they would have had a bunch of scrolls stored together. So, someone just grabbing all the scrolls indiscriminately could easily think they were all meant to be read the same, with equal authority and equal utility.
Obviously, not everyone would agree with either or both writers. I find that it's a sensible position to hold even if one thinks it isn't what happened.