The edtech community has promoted claims that digital education enhances access, learning, and collaboration. The COVID-19 pandemic tested these claims like never before, as higher education systems seemingly overnight had to move teaching online. Through a sequential mixed-method approach, we investigated how 85 higher education leaders in 24 countries experienced this rapid digital transformation. Through their experiences, we identified the multiple and overlapping factors that contribute to an institution's ability to realize the potential of digital education, in terms of access, learning and collaboration, whilst highlighting deeply rooted inequalities at the individual, institutional and system level. Drawing on these empirics, we put forth recommendations for closing the digital divides and pathways forward. Higher education leaders are uniquely positioned to move beyond the emergency adoption of online learning towards inclusive, long-term visions for digital education, which emphasize collaboration over individual gain.