Digital technologies allow student self-assessment to be adaptive, scalable and multimodal. Despite such technological advances, digital self-assessment practices have largely reinforced the existing norms around student roles, leaving the fundamentals of self-assessment design untouched. Digital self-assessment has centred on learning outcomes and self-regulation with less attention to students' own initiatives, aspirations and roles -- their agency. Ironically, the 'self' has remained at the margins of digital self-assessment work. In this conceptual study, we propose 'the digital' as a catalyst to rethink the student role in self-assessment. This way, the digital could address fundamental issues with self-assessment already present in the pre-digital age. We explore three ways in which digital self-assessment could promote student agency. By reviewing critical examples of literature on self-assessment and digital technologies, we propose that the digital in self-assessment may be seen: (1) as a tool for promoting students' self-regulation, as understood in individualistic terms; (2) as a means to develop students' digital agency; and (3) as a means to provide students with agency over their identity formation in the digital world. These three ideas may guide future work to ensure self-assessment design is relevant for students' increasingly digital futures, particularly in an era of Artificial Intelligence.