I would suggest that the seeming contradiction SpiritMeadow questions is corrected by a slightly broader reading of the worth of the ancient writings than AspiringDeacon’s post would allow. Can’t we agree that the writings show what was taught and believed in at least some parts of the ancient Church at the time they were written and used? Where those teachings match, or are close to, today’s teachings we can point to the consistency. That is meaningless unless we can point to places they don’t match and note the inconsistency.
Each ancient writing can only serve as evidence of beliefs at the time and place that it was written and used. If the existence of a teaching at variance with modern teaching in an ancient writing does not tend to show that the teaching varied (at least at that place and time), then the existence of a consistency cannot show the opposite.
This inconsistency does not, in itself, call the teaching into question, of course, but it does reveal something about our history and early formation. So clearly they have important historical relevance. The tougher question is whether they have any theological or spiritual significance (beyond proving the longevity, or lack thereof, of a particular belief).
I think that they can, but in a limited way. Perhaps it is nitpicky, but I would not refer to these works as “non-inspired.” We know that the canon was inspired, because according to dogma the fact that the Church included them is infallible evidence of inspiration. We don’t know, I think, that other works were not inspired. Some works, such as the Apocalypse of Peter, were widely accepted in the early Church, and failed to make the canon. (Maybe they didn’t want two Apocalypses? Maybe they decided it wasn’t really inspired? I don’t think we know why.) At least two Apostolic works, additional Epistles of Paul referred to in the existing Epistles to the Corinthians, were either lost to time before the canon or discarded as not useful, but surely were as inspired as his other writings. None of that is to say that any Catholic should accept something in a non-canonical work that is at odds with the canon, but I think that if read in proper context they can serve as more than historical oddities.