To me it is all about the writing. They are well written so children learn sentence structure, punctuation, and most importantly to me VOCABULARY! They use words in classic writing we don't hear anymore. Having a good vocabulary is SO important.
Just a funny tidbit
I worked at a college and one of the students was a work study in my office. At lunch one day she was asking me about some words she was taught in school in South Korea. She wanted to know if I ever used them... or if any Americans used them. I explained to her that some Americans knew them and used them but the VAST majority just didn't. It is sad really. I am not a reader but I have a very good vocabulary and I plan for my children to have a better vocabulary than their parents.
I'm a huge reader, or was, these day's I'm an author as my day job and don't have much time to read books, as I spend more spare time on BYC or with my animals/video games..
I've never read the classics, and I usually have both a dictionary, and a thesaurus open to help me make sure I use a wider variety of words as an author, and to make sure i'm using them in the correct context, due to my dyslexia, because of not using them in day to day life.
As it is, my husband routinely tells me not to use such big words with small children, because I use words that are often too advanced for the listener.
However, in my case, I'm autistic, and I literally cannot dumb down how I speak for children, so I use too big of words. LOL But, I never got that from reading the classics, I got that just from reading in general.
I do think that the average person, didn't read the dictionary, like I did as a kid because I wanted to figure out new words, that I could use for fun. I thought it was funny to find words no one else knew and had to look up.

I didn't know that reading and memorizing the dictionary, was considered odd, as a kid!
My 5 year old isn't reading yet, but she has a very good grasp on language, better than her 12-year-old brother actually, who does read a ton, including classic stories like "to kill a mocking bird" and "ann frank diaries."
I would say that understanding language, is more from using it, then just reading it. If you don't use the words you hear, read, or look up, the knowledge kind of goes in one ear, and out the other.
For example, I'm teaching sign language, and my kids are learning Spanish. I cannot keep a second language with out using it on a regular basis.