Let me try to answer your questions:
1. I think you misunderstand what a structure is. A structure is not meant to mirror a "solution"! So structuring a case does not mean to brainstorm all sorts of buckets and possible answers and then hope that one of these is actually "correct". A structure is meant to explain, how you will answer the precise question asked by the client. So a structure is a logic! And you are asked to lay out this logic, according to which you will answer the question. If you follow this principle, then the problem you described completely vanishes. A sound top-down logic includes (i) the question, (ii) the criterion to answer this question (derived from the underlying objective!), and (iii) the logical disaggregation of the criterion's elements to eventually test if it is met or not.
2. The "process" on how to start into the case is (mostly) exactly as described in Case in Point. However, the actual approaches ("frameworks") are very weak in this book - mostly due to the fact that they ignore what I outlined under 1. above. Just laying out buckets and areas to look into is a purely explorative way of working (defining areas, and then looking into these areas in the mere hope to find something interesting that will lead you on the right track towards solving the case; another word for this approach is 'guessing') - and if one is mean one could say that this exactly how your should NEVER work as a strategy consultant. That being said, the frameworks are still quite helpful for beginners in order to get a good feeling for the areas that will most probably be relevant in the actual analysis in certain contexts.
3. The time is not super critical. Crafting good and robust structures usually takes around 90 seconds for a well trained candidate. But even if it takes longer - I can promise you that, if your approach is a super clear top-down explanation of how you will answer the clients question, what you will analyze and what are the most important qualitative areas to explore in order to perform this analysis, then every interviewer will immediately forget about any doubts he might have had on your speed. My mentees usually take far more than a minute to structure, and it is never standing in the way of getting MBB offers.