Increasing profitability is a common outcome most clients are trying to achieve when they hire consultants. Its wrong to assume that a profitability case would be easier to solve than other case type. However, the initial framework i.e. R-C is easier to envisage and most often that it is applicable. Firms are testing you on structure, critical thinking, communication etc. so the case type really does not matter.
Its important to come up with a multiple hypothesis in a profitability case and seek information to prove it and move to other branches of analysis if the data indicates that your original hypothesis was incorrect.
Profitability framework might help you to identify the root cause but while providng insights into how the company can increase profitability you would need employ a different framework , such as delving into customer (new distribution model for reaching consumer , improve customer experience), competition (entry of new competition or alternate product substitutes), cost (reduce raw material cost, reduce cost through economies of scale) etc.