I feel like after graduate students pass their qualifying exams, they still have a lot of learning to do before they're knowledgeable enough in a specific area to understand and work on the open questions in that area. But how do they get there? Do they just take advanced courses in the area of interest, or are they expected to read up on their research area outside of coursework? If the second, should they be doing this while they're still taking classes, or do they start doing this after they're done with their coursework?
Yes, you're right, "starting research" prior to an adequate basic education can result in huge wastes of time. But it also makes little sense to "wait a few years" until all the required coursework is done. And, yes, even then, one is not over-educated.
Seriously, I think (and recommend to my students) that they maintain several different threads. The two main ones are attention to standard core material and more advanced courses, while also trying to skip forward to read about current events. The trickier third thread is trying to back-fill from current events to "standard material", as needed.
Almost any choice of "single thread" seems misguided.
It depends. My PhD supervisor got me involved from Day 1 in research projects in his lab. He was down on programs where things were much more serial (do the required classes, pass the qual, do a proposal, do the research, defend). His students all had some research tasks from the beginning. If the student was unprepared for the task, there were papers to read or book suggestions, etc. This worked really well for me, though it may have resulted in me being somewhat under-prepared for the quals the first time I took them! I eventually passed and graduated.
Some advisors and programs take a different approach. They really want the student to concentrate on nothing but getting through courses and the quals until they pass the quals. Then it's the proposal (if they require one). How one gets the knowledge to get from proposal to defense is up to the student and the advisor to work out. I didn't complete my coursework requirement until late in my program, so I used courses to close knowledge gaps where a relevant course was available. Where it wasn't, I worked through books and papers that I could find that helped.
While I totally agree with the other answers, I would like to point out that there is a third variety out there in the market as well, over and above the two major approaches to coursework already pointed out. At least to me, this appears to be a more evolved approach, but of course, neither one is flawless and universally applicable (i.e. a lot depends on individual cases).
The idea is - first figure out how much do you need to get started with proper research-level work. This would be difficult for the student to work out on his/her own, and definitely requires inputs from the adviser. Once this part has been marked out, this should be approached at full throttle, i.e. no actual research till this part is behind you. After this is done, and in parallel with the actual research work thus started, keep on expanding your sphere of knowledge. A good idea is devote a stipulated number of hours everyday, forcibly detaching yourself from the actual problem, and just reading around the part you people decided on as minimum. The more you know, the better prepared you will be for your research, but it is not sensible to wait indefinitely for the same to happen, especially since there are (typically) progress metrics also involved (or something like an end-semester presentation of the work done in that semester, etc.).
IMO, the advantage of this strategy is - you are not deferring research work unnecessarily, and also, not just hitting on a research-level problem without being in any position to do so. And with time, the situation certainly gets better and better.