Especially since the onset of the COVID-19 pandemic, the use of cloud-based tools and solutions - lead by the ‘Zoomification’ of education, has picked up attention in the EdTech and privacy communities. In this paper, we take a look at the progressing use of cloud-based educational tools, often controlled by only a handful of major corporations. We analyse how this ‘cloudification’ impacts academics’ and students’ privacy and how it influences the handling of privacy by universities and higher education institutions. Furthermore, we take a critical perspective on how this cloudification may not only threaten users’ privacy, but ultimately may also compromise core values like academic freedom: the dependency relationships between universities and corporations could impact curricula, while also threatening what research can be conducted. Finally, we take a perspective on universities’ cloudification in different western regions to identify policy mechanisms and recommendations that can enable universities to preserve their academic independence, without compromising on digitalization and functionality.