Of course, it does force us to keep the teaching in mind while reading the book and be aware of Lippmann's use of the word allegory.
I may not have my word count right, but the first time I came across "allegory" in the book is in the third paragraph of chapter eleven, where the author writes:
"The bewildering variety of our impressions, even after they have been censored in all kinds of ways, tends to force us to adopt the greater economy of the allegory. So great is the multitude of things that we cannot keep them vividly in mind. Usually, then, we name them, and let the name stand for the whole impression. But a name is porous. Old meanings slip out and new ones slip in, and the attempt to retain the full meaning of the name is almost as fatiguing as trying to recall the original impressions. Yet names are a poor currency for thought. They are too empty, too abstract, too inhuman."
What struck me reading this is that one level of the teaching of the cave may be lost on me to the extent that I participate in the allegory, a form of thought itself a kind of prison of the mind.