I personally interpret the sentences in a similar way to "look in something for". The phrase "look in something for" is most often use as meaning opening a container and attempting to find a specific object within:
I looked in the glove box for my sunglasses.
She looked in her purse for her keys.
He looked in the nest for baby birds.
The "for" in each case expresses the object which is the purpose of the looking. There is an implication that there's some larger reason for you looking, but not necessarily what that reason is (e.g. why you are looking for that object). In some cases, simply confirming the presence of the object in the container is the purpose. You might not even need to extract that object from the container.
"Look in" is not unique in this respect. "Look at", "examine", "search", etc. all can take "for noun" as a modifier, where "noun" is the object (thing or abstract concept) which prompted the search.
I would interpret the two clauses with "read" in the same way. "I read poems for grammatical correctness" to me implies that "grammatical correctness" is a thing which the "container" of the poems contain, and one is looking within the poem to locate it. (Why one might be looking for grammatical correctness is left unsaid but unneeded - the implication is that the poems don't contain it, regardless of the "why"). With this interpretation, "I don't read poems for grammatical correctness" parallels "I don't look in nests for baby birds."
Personally, I interpret "I read poems for pleasure" as even more a metaphor. The poem doesn't actually contain the pleasure. The pleasure is generated purely on the reader's side in the process of reading. But after reading it effectively looks like the reader has opened the container of the book, and found a "pleasure" object within.