Self-supervised speech models such as wav2vec2.0 and WavLM have been shown to significantly improve the performance of many downstream speech tasks, especially in low-resource settings, over the past few years. Despite this, evaluations on tasks such as Speaker Diarization and Speech Separation remain limited. This paper investigates the quality of recent self-supervised speech representations on these two speaker identity-related tasks, highlighting gaps in the current literature that stem from limitations in the existing benchmarks, particularly the lack of diversity in evaluation datasets and variety in downstream systems associated to both diarization and separation.