When I find a pattern in a work of fiction, I’m pulling on a thread that the author has woven into the text. How far does such a thread extend? Does it have meaning apart from the instances I’ve spotted?
In the sciences, we rarely have to check that, because we’re trying to extract a law of nature. Natural laws are true all the time, so when I’ve found a pattern, I’ve accomplished something. I can extrapolate from it without fear, as long as I remember the domain of validity of my Ansatz.
With a work of fiction, by contrast, there is no reason to suppose that I’m working within an inductive set, from which I can infer future things. Once the text ends, what reason is there to suppose that the pattern I found goes any further? This is where so many literary analyses fall down. A pattern I see in one place may not be a fundamental symmetry that applies anywhere else.
Now, searching for patterns to go across multiple texts has merit. In fact, that’s how genres get defined. But that’s the domain of the real literati, not “trespassers”. (To borrow JRRT’s characterization in “On Fairy-Stories”.)