Forgive me for being unclear earlier but it is in the verbage.
In the links below, for instance, >The expression by means...>a representation... figurative treatment...>a narration or description of...
The idea is that there has to be someone Expressing, representing, treating, and, most directly, narrating the description of the allegorical representation.
Perhaps this link explains better explains, and even notes the reader's interpretation. Notice how it mentions at the beginning that it is a "symbolic, fictional narrative," (in other words, a narrative intentionally created to be symbolic), and later refers to allegory as a literary device. Therefore just as, say, metaphor or simile is intentionally chosen by an author, so too is allegory, on a larger scale.https://www.britannica.com/art/allegory-art-and-literature
I.e., you can't have Plato's Allegory of the cave without Plato making the Cave Allegory, but you could, on your own, interpret a shadow on a cave as the surrounding world being a shadow, an idea he did Interpret for himself before he made an intentional allegory. I hope that helps clear things up!