I wouldn't say that you should just study and study and never do the word. But I would say that the context of the passage in question is more about a teacher studying to be approved to God as a teacher. Hence the phrase "a workman that needeth not to be ashamed" and specifically "rightly dividing the word of truth." So, you are right that you don't just study to study. But you are stepping away from the context of the passage in question a bit too far I think. At the same time, I grant you that "be diligent" (along the same lines as the KJV renders the same base word in 2 Tim 4:9 and Titus 3:12) or even "labor" (as the KJV renders in Heb 4:11) would not be wrong translations. However, I think "study" fits the context very good here, even moreso than "be diligent." "Be diligent" is weak in connotation although the denotation is ok. It sounds too much like a state of mind rather than an actual effort. So, really, "be diligent" is the least favorable translation. "Labor" certainly beats it by far! Yet, study, being that is has the double sense, seems more to fit the context.