It is true that the ultimate purpose of studying is to do the word, but you are ignoring the very verse you are writing about. Why go all the way back to Ecclesiastes when you can look at this verse itself 2 Tim 2:15 "Study to show thyself approved unto God, a workman that needeth not to be ashamed, rightly dividing the word of truth." Study to do what? Show thyself approved. Approved in what way? Being a workman that has no need of being ashamed? Why not? Because he rightly divides the word of God. So, in this verse, rightly dividing the word is the purpose of the studying, which (BTW) makes your argument that study is a wrong translation very funny. First, study still has both senses today (1) be diligent and (2) read, compare, whatever, so it is silly to say that study is wrong. Secondly, because it still contains both senses it is preferable to "be diligent" because "be diligent" is just the translational suggestion of those who try and claim that study in the sense of reading is unnecessary. Third, Paul gave a similar instruction to timothy in the first letter, 1 Tim 4:13 "Till I come, give attendance to reading, to exhortation, to doctrine." These are basically parallel passages, Paul's exhortation to Timothy to study to show himself approved as one who rightly divides the word and his exhortation to have him "give attendance" to reading, etc. these are the same thing.