Self-supervised learning (SSL) leverages large datasets of unlabeled speech to reach impressive performance with reduced amounts of annotated data. The high number of proposed approaches fostered the emergence of comprehensive benchmarks that evaluate their performance on a set of downstream tasks exploring various aspects of the speech signal. However, while the number of considered tasks has been growing, most proposals rely upon a single downstream architecture that maps the frozen SSL representations to the task labels. This study examines how benchmarking results are affected by changes in the probing head architecture. Interestingly, we found that altering the downstream architecture structure leads to significant fluctuations in the performance ranking of the evaluated models. Against common practices in speech SSL benchmarking, we evaluate larger-capacity probing heads, showing their impact on performance, inference costs, generalization and multi-level feature exploitation.