pakeha
The documents we're considering are devotional literature, correct me if I'm wrong. What kind of historian uses devotional literature as source material for the historicity of the object of devotion?
There's a subtlety here,which I hope you don't mind my pointing to. Just as the basic problem with an HJ is that Jesus is interesting to us almost entirely because of what people did with his legend after Jesus had paid his debt to society, some literature is designated "devotional" chiefly because later people used it in their devotions. The authors may be innocent.
The Epistles of Paul are mostly business correspondence,
Romans being the exception, a learned treatise and model of high prose comporsition. The author was devoted to a form of Christianity (which we have every reason to think was absorbed by later versions, even before he died), but his readers were apparently still "searching," based on Paul's complaints.
We don't know why "Mark" wrote
Mark, we just know that some other people liked the story well enough to read it aloud in church.
Matthew, too, whose hash of the Jewish scriptures is sufficiently bad that some people propose non-religious original intent.
Luke-Acts appears to have been written as a work for hire for a specific client - perhaps a hiring more analogous to one spouse engaging a private detective to check up on the other spouse, rather than catechesis.
John is alone among the canonical Gospels in describing itself as a work of public instruction in the faith.
What is "core"
Thomas? A book of sayings. The Coptic translation that reaches us has lots of accretions (no Jewish rabbi taught some of those things), and the accretions bespeak a devout Gnosticism, but the "core" isn't so different from the collected sayings of, say, Epictetus. Nobody calls Epictetus "devotional" (although he seems to be profoundly devout in
his religion, which is no longer practiced). Why not? Because he isn't read in church, a matter over which he has no control.
Once we're safely near or beyond the turn of the Second Century, and the canon is mostly closed except for late hits and forgeries, frankly never-devotional material becomes relevant. Examples are Pliny-Trajan, churchly business correspondence (
1 Clement is, like Paul, thumb-wrestling with the Corinthians, this time over some poorly specified point of church governance or discipline), and
Acts of ... works, which are ripping yarns with stock characters whose names and backstories are borrowed from the canon.
Assuming that that view of the literature is justified, the taint of "devotional" may be exaggerated. In fact, we know it is exaggerated, since
Mark is often cited interchangably with
John when the subject of miracle stories is discussed. Similarly, dismissal because it's all apologetics is bizaarre - who the hell writes about anything unless they have an opinion about the subject?