The basic premise of your question is wrong. You are never asked to "create a framework"! The first question of the interviewer will most likely be to show him how you would approach and answer the client's question. THis means, you are asked for a LOGIC, not for a set of areas. This is a big big misunderstanding of most candidates. Structuring a case means (1) narrowing down the core question and (2) making explicit the LOGIC according to which this core question will be answered. Areas and "buckets to look into" are just a by-product of this logic.
So if your logic is sound, then it will of course include all relevant aspects that need to be tested to arrive at an answer. In an interviewer-led case, the interviewer just directly points you to the area he wants to focus on by means of a concrete question (this is then the second question, after the one mentioned above).
This means that, in order to robustly build your case solving muscle, you HAVE to learn it in the interviewee-led way. You can not learn proper case solving by focusing on interveiwer-led cases. However, once you have built the necessary skills, these interviewer-led cases are much easier, because they have much less contingency and complexity in terms of navigating through the branches of your logic.