Although probing frozen models has become a standard evaluation paradigm, self-supervised learning in audio defaults to fine-tuning {when pursuing state-of-the-art on AudioSet}. A key reason is that global pooling creates an information bottleneck causing linear probes to misrepresent the embedding quality: The $\texttt{cls}$-token discards crucial token information about dispersed, localized events in audio. This weakness is rooted in the mismatch between the pretraining objective (globally) and the downstream task (localized). Across a comprehensive benchmark of 13 datasets and 6 spectrogram-based encoders, we investigate the global pooling bottleneck. We introduce binarized prototypical probes: a lightweight and simple pooling method that learns prototypes to perform class-wise information aggregation. Despite its simplicity, our method notably outperforms linear and attentive probing. Our work establishes probing as a competitive and efficient paradigm for evaluating audio SSL models, challenging the reliance on costly fine-tuning.