Are undesigned coincidences fabricated?

One objection to the Gospels as historical sources is the claim that these aren't four independent biographies. rather Matthew and Luke simply copy Mark for some of their material, while John invents other stuff. Likewise, that Matthew and Luke embellish Mark's stories. 

It is, of course, true, that Luke uses Mark as one of his sources while Matthew is very familiar with Mark. But there's more going on.

When two or more observers witness the same event, their respective accounts will sometimes dovetail in subtle ways. Between 23-26 min mark:

https://www.youtube.com/watch?v=92QqWPcq8z0&t=5s

Peter Williams has a clear exposition. I'm going to piggyback on his exposition. The basic idea is that undesigned coincides reflect independent knowledge of the same event. 

Critics like Richard Carrier have responded by claiming that Matthew, Luke, and John invented the "undesigned coincidences" to give these accounts the appearance of factuality. In historical fiction, the author sprinkles his story with factoids to make it seem more true to the time and place.

However, a basic flaw in that response is that undesigned coincidences are far too subtle for the vast majority in the audience to catch. To begin with, most members of the original target audience for the Gospels didn't own personal copies of the Gospel. That's why the the public reading of Scripture is an ancient custom of the church. We're talking about listeners rather than readers. They heard the Gospels read aloud. Imagine mentally comparing and contrasting the Gospels at the level of undesigned coincidences. How realistic is that? 

But even when we get to the era in which many Christians have private copies of the Bible, the coincides are too oblique for the vast majority of Christians to notice. You must be an extremely attentive reader to pick up on the coincidences. If the purpose of undesigned coincidences was to make the accounts look factual, this is a completely ineffective method inasmuch as precious few readers are sufficiently observant to register the coincidences. What historical fiction authors do that?