In the field of continual learning, models are designed to learn tasks one after the other. While most research has centered on supervised continual learning, recent studies have highlighted the strengths of self-supervised continual representation learning. The improved transferability of representations built with self-supervised methods is often associated with the role played by the multi-layer perceptron projector. In this work, we depart from this observation and reexamine the role of supervision in continual representation learning. We reckon that additional information, such as human annotations, should not deteriorate the quality of representations. Our findings show that supervised models when enhanced with a multi-layer perceptron head, can outperform self-supervised models in continual representation learning.