You are right - such a laundry list of buckets to look into feels (and actually is!) completely arbitrary.
A structure to approach a case should be rooted in the actual question that you need to address. From there, you should define the criterion to answer this question, and build a corresponding value driver tree with branches and sub branches. All the elements that you have listed above (market structure, target company operations/capabilities, synergy levers, etc.) should be mapped to the different sub branches of your value driver tree. This is true, regardless of whether you are looking at a PE/M&A scenario, or market entry, or capacity expansion, or new product launch, etc. etc.
The crucial point is that, thereby, you create a rigorous thinking frame which organizes all relevant elements into a structure by which you can link the analysis of every element back to the core question you need to answer by means of logic.
Unfortunately, no case books are revealing this to candidates, creating the illusion to candidates that "learning frameworks" is an acceptable approach towards cases.