Personally, I suspect other reasons far outweigh that.
However, I believe with almost any reasonable measure you choose, the KJV Bible has a very high literary value. Even Richard Dawkins would acknowledge that. [1] And for what it's worth, I am not a Christian, so I don't think I am biased by religious zeal or something.
I suspect people think so mainly because besides Shakespeare, that's the only thing most people know of that's written in this "cool" archaic language. Like Shakespeare, it's just on the limit of still being understandable, but full of thees and thous, which, the more people don't understand it, they love it all the more (as witnessed by the usage errors they commit when trying to use it, which judging from what I see online are more freqent than the cases of correct usage).
But when this particular edition was written it was in pretty much ordinary everyday language. And the stories themselves are the same old "vengeful old arsehole on a cloud smites sometimes his beloved semi-barbaric nomadic bronze-age shepherd people, sometimes their enemies" as in all other editions, so "great" as literature? Naah, I still just can't see it.
What "reasonable measure", exactly, makes it so?
> And for what it's worth, I am not a Christian
I am -- in name only (that's the first C in my username). I still believe in nominal determinalism in some cases, though certainly not in my own.
> so I don't think I am biased by religious zeal or something.
I am, all too often. Of the anti- kind.