Privacy is a multi-faceted, interdisciplinary concept, with varying meaning to different people and disciplines. To most researchers, anonymity is the ""holy grail"" of privacy research, as it suggests that it may be possible to avoid personal information altogether. However, time and time again, anonymization has been shown to be infeasible. Even de-facto anonymity is hardly achievable using state-of-the-art cryptographic anonymization techniques. Furthermore, as there are inherent tensions between the privacy protection goals of confidentiality, availability, integrity, transparency, intervenability and unlinkability, failed attempts to achieve full anonymization may make it impossible to provide data-subjects with transparency and intervenability. This is highly problematic as such mechanisms are required by regulation such as the General Data Protection Regulation (GDPR). Therefore, we argue for a paradigm shift away from anonymization towards transparency, accountability, and intervenability.