I’m from Asia – specifically from one of the most exam-oriented nations, Singapore, which frequently pops up near the top of the PISA rankings alongside Finland –, and I did grow up with TOEFL books on my shelves, though I was never forced to study them. (Granted, my parents were exceptions in a society where many are afraid of falling behind and losing out.) While they certainly initiated me into prefixes and suffixes, and started me on my long (and continuing) journey of investigating and loving etymology, I still don’t think anyone actually studies them as their primary source of English knowledge. Tell me if you have contradictory evidence, by all means (even if it’s just anecdotal), but I really think that even test-obsessed Asians don’t study those alone, particularly if they have any experience with real English usage or have visited an English-speaking country. Singapore’s everyday English may be far from standard, but our English textbooks and workbooks aren’t particularly SAT- or TOEFL-like, even if they include plenty of exercises and grammar. I’d like to believe that the only people who regularly do TOEFL/SAT drills are those aiming for high scores on those tests (I’ve known some of them), without necessarily expecting those test-taking skills to translate into real English ability. (Though of course, the TOEFL and SATs are probably slightly more reflective of actual language ability than the JLPT due to the test format, so it’s hard to compare.) My understanding is that Asians drill for those tests, even when they know their home country’s syllabus is far beyond what’s required in a given subject area, for the sole purpose of maximising the utility of the test score, be that in order to enter a prestigious university or to impress prospective employers with their scores. That’s understandable if you’re from a culture where a single mark can change everything, which is certainly the case in densely-populated nations like China, or in Japan, which has a university entrance exam system.
Perhaps I’m just blissfully ignorant of what my Asian peers are doing, but as far as I know, no one, even in the most competitive societies like Korea, China and Japan, can reasonably be drilling test prep books alone, if only for the reason that I’ve seen what language textbooks are like in Japan (for French), and they’re ridiculously far removed from TOEFL and SAT formatting. Japanese people don’t study languages like that: they do pattern drilling and formatted conversations, coupled with grammar exercises. I really doubt that language instruction in China or Korea is far off. Furthermore, if they actually drilled TOEFL effectively, they would probably have a much wider vocabulary (I know since I’ve seen what some books contain), which isn’t what I’m seeing from my personal experience (as a tourist, which doesn’t say much) and from my friend’s experience studying at one of the top universities in Japan.
In any case, and in all fairness, I think I can counter that many people believe doing well for the JLPT is something to be proud of (it is) and that it’s proof of being proficient in Japanese (it isn’t, though it can be an indicator). There are plenty of stories of people with JLPT N1s being unable to hold a conversation, and even rumours of Chinese people with no Japanese knowledge passing the N1 using their kanji knowledge alone. (I think the second is an exaggeration, but it’s true that for an advanced test, most questions will be written in kanji, which helps immensely – I’m a Chinese speaker, so I should know.) My main point was that regardless of ethnicity, culture of origin, beliefs on the value of hard work or test-taking priorities, the idea of using test prep books as one’s main source of language instruction is misguided, even if it’s certainly possible to use them to improve (as I did while preparing for my DALF C2 examination for French) and to work on specific details of a target language. If, however, OP feels that the JLPT is an important goal, then I would encourage OP to consider getting test prep books like the Shinkanzen Master series and to study them seriously, but not exclusively.