One effect of using no quotation marks to signify direct speech is to keep all of the letters/entries (written by Celie) directly aligned with Celie's own narrative - her own telling.
The novel is, essentially, Celie's story and her character relates the great majority of the material to the reader as the narrator of her letters. Celie's interior, emotional life is very much a subject of the novel and, as such, justifies a formal choice not to objectify the novel through "third-person tools" like quotations marks.
Eschewing the quotation marks, Celie's story remains her own and is told formally in her own voice.
Celie's education is also on display in her writing and this is another point to consider if we ask, not why does Alice Walker choose not to employ quotation marks, but why Celie chooses this method of narrating dialogue.
The rural, idiomatic speech used by Celie contrasts dramatically with the standard English used by Nettie, and it illustrates graphically how a change in environment can affect something as fundamental as language. (eNotes)