I was wondering whether, at the beginning of a case interview, it would be appropriate to use rather theoretical graphs in order to visually translate the interviewer's question, or whether it might seem odd.
So, for instance, for a market entry case, I might show the interviewer that the company must position itself on a matrix.
The two axes of this matrix are: market attractiveness and importance (of a certain product) to customer.
So, ideally, the company would want to position itself in an attractive market and have a product, plus company resources, skills, experience etc. valued by the customer, which would optimise its ability to win in this market.
Similar to the BCG-Matrix, this is one of the "general frameworks" which just visualise the client's problem. Would it be appropriate to bring those in and if so, when and how to do it the best?
Using visual aids like a 2 x 2 matrix such as the one you describe above is fine...when appropriate.
So what defines appropriate?
When using such a tool is relevant to the issue discussed in the case.
In fact, when it is relevant, it is very useful to use visuals such as a 2x2 matrix or other visual aid tools to convey your point.
However, where this backfires is when the use of a particular tool is not relevant but the candidate tries to force the use of the tool anyway.
So in your example above, if "attractive market" and "importance of product to a customer" are in fact the two key factors, then using a 2x2 matrix is appropriate.
But if the actual key factors are the client's competitive advantage, the under-served nature of a particular customer segment, and a barrier to entry keeping existing competitors from entering the market, then a 2x2 matrix using "attractive market" and "product" would not be relevant.
So the rule is decide what is relevant first, then figure out how to best communicate it -- visual tools are great to communicate your point.
They are not a substitute for critically thinking about what is important in a particular case situation.