Different organisations recently published reports identifying the challenges and potential solutions to ensure privacy in blockchain platforms. The proposed solutions frequently emphasise the role of privacy-compliance technologies to be incorporated into the blockchain design. Often, these solutions imply a techno-regulatory approach, ignoring that the level of privacy implemented in a blockchain involves legal and policy choices, disregarding the need to implement human participation and contestability in these platforms. Against this backdrop, this paper proposes to examine how privacy-compliance technologies can incorporate human participation and contestability: first, resorting to the interdisciplinary literature to examine how technological design could balance privacy with human oversight; second, discussing the challenges to ensure ex post contestability for aggrieved data subjects; third, examining the difficulties in identifying liable parties in a blockchain platform. The current disregard of the social and human element risks undermining the role of privacy-compliance technologies in the blockchain.