Daniel R. Street has an excellent post on "reading" Greek as it relates the teaching of the language. My favorite part, describing what is wrong with "grinding" through Greek:
The student is focused on form, grammar and syntax, and often on analyzing, labeling or parsing various elements, not on comprehension. Indeed, comprehension is delayed until the translation into English is completed and can be read by the student.
The struggle is to transform Greek pedagogy so that it encourages reading. However I suspect that there is also the hurdle that some pupils will not really want to learn how to fluently read Greek.