This paper presents a sociotechnical vision for managing personal data, including cookies, within Web browsers. We first present our vision for a future of semi-automated data governance on the Web, using policy languages to describe data terms of use, and having browsers act on behalf of users to enact policy-based controls. Then, we present an overview of the technical research required to {prove} that existing policy languages express a sufficient range of concepts for describing cookie policies on the Web today. We view this work as a stepping stone towards a future of semi-automated data governance at Web-scale, which in the long term will also be used by next-generation Web technologies such as Web agents and Solid.