Public investment, through both research grants and university funding, plays a crucial role in the research and development (R&D) of novel health technologies, including diagnostics, therapies, and vaccines, to address the coronavirus disease 2019 (COVID-19) pandemic. Using the example of remdesivir, one of the most promising COVID-19 treatments, this paper traces back public contributions to different stages of the innovation process. Applying the Risk-Reward Nexus framework to the R&D of remdesivir, we analyse the role of the public in risk-taking and reward and address inequities in the biomedical innovation system. We discuss the collective, cumulative and uncertain characteristics of innovation, highlighting the lack of transparency in the biomedical R&D system, the need for public investment in the innovation process, and the "time-lag" between risk-taking and reward. Despite the significant public transnational contributions to the R&D of remdesivir, the rewards are extracted by few actors and the return to the public in the form of equitable access and affordable pricing is limited. Beyond the necessity to treat remdesivir as a global public good, we argue that biomedical innovation needs to be viewed in the broader concept of public value to prevent the same equity issues currently seen in the COVID-19 pandemic. This requires the state to take a market-shaping rather than market-fixing role, thereby steering innovation, ensuring that patents do not hinder global equitable access and affordable pricing and safeguarding a global medicines supply.