What potential downside occurs when incorporating a pipeline within cross-validation?

Incorporating a pipeline within cross-validation leads to the elongation of the runtime primarily because each fold requires refitting all stages of the pipeline. This means that for every partition of the data used in cross-validation, the entire pipeline, which may include data preprocessing, feature selection, and model training, must be executed anew.

While pipelines enhance the structure and reproducibility of the machine learning workflow by encapsulating all steps of data processing and model training, this also entails significant computational costs during cross-validation. Each fold involves training the model from scratch with transformed data specific to that fold, which can markedly increase the total computation time required to evaluate the model's performance.

This is a valid consideration when balancing the need for model evaluation against the computational resources available, making option C the most appropriate choice in terms of understanding the impact of pipeline integration during cross-validation.