The (academic) world is divided into those who think that we are teaching our students too little and those who think we are teaching them too much. Specifically, if one looks at graduate school, there are those who feel that we can start students on a juicy research problem and then they can pick up whatever they need along the way, and then there are those who feel that a certain core programme of study is "essential" in order to tackle new problems in a novel and meaningful way.
As usual both groups are right --- and so both are wrong as well!
One way to approach the problem is to look at what has evolved as a way of determining the course work that forms a component of a research programme. The faculty out of which the research advisor of the student will eventually be picked tries to form a consensus on what constitutes a core syllabus for their subject of research. Each faculty member provides an input based on her/his own experience and requirements. However, in a very broad-based such a consensus may be hard to arrive at and may be a "compromise" solution. Again, if the compromise is "peaceful" this may be fine, but a compromise that is acrimoniously arrived at may leave bitter feelings. It may be better to decide to leave space for optional courses which are more specialised even in this "core". Eventually, if there is enough divergence of interests then it may be necessary to propose the division of the faculty along some boundary. As is well-known, such a decision is fraught with problems of its own --- financial and numerical viability being the primary concern of each half.
Hence, let us propose an alternate way in which one can decide on the course of study. The magic of the marketplace. (To use a phrase I heard from Nitin Nitsure). Even the most goal oriented research labs will not hire a person whose only credentials are research papers --- unless we are looking only at the tails of the distribution. At the same time a scholar who has little or no published research will find obtaining a job in even the most academic and teaching oriented department rather difficult. So it seems that the marketplace does demand a suitable mixture of both.