This question probably depends on who is asking? Does it matter to whom?
– Does it matter to someone who is already Christian? Perhaps not much?
– Does it matter to someone raised in a Christian home, Sunday School, church? Depends how much questioning they have done.
But to the original audiences for whom the books of the New Testament were intended for 2,000 years ago, the question of who wrote the 27 books was fundamental. For the original audiences inspiration was a not a vague concept but a physical one, rooted in the idea that these men were inspired, not the book itself, divorced from the authors.
Take for example:
– Matthew and Mark as the two Jewish witnesses required by Jewish law
– the Greek Luke satisfying Theophilus that he had carefully interviewed eye witnesses
– John in both Gospel and Letters repeatedly stressing that he and the others were eye witnesses of the Word
– Paul recounting his eye witness vision experiences with Christ in his letters
In each case the reality of eye-witness to claim inspired authorship does matter.