Ontology-based question generation is an important application of semantic-aware systems that enables the creation of large question banks for diverse learning environments. The effectiveness of these systems, both in terms of the calibre and cognitive difficulty of the resulting questions, depends heavily on the quality and modelling approach of the underlying ontologies, making it crucial to assess their fitness for this task. To date, there has been no comprehensive investigation into the specific ontology aspects or characteristics that affect the question generation process. Therefore, this paper proposes a set of requirements and task-specific metrics for evaluating the fitness of ontologies for question generation tasks in pedagogical settings. Using the ROMEO methodology, a structured framework for deriving task-specific metrics, an expert-based approach is employed to assess the performance of various ontologies in Automatic Question Generation (AQG) tasks, which is then evaluated over a set of ontologies. Our results demonstrate that ontology characteristics significantly impact the effectiveness of question generation, with different ontologies exhibiting varying performance levels. This highlights the importance of assessing ontology quality with respect to AQG tasks.