Since the onset of the COVID-19's global spread we have been following the debate around contact tracing apps -- the tech-enabled response to the pandemic. As corporations, academics, governments, and civil society discuss the right way to implement these apps, we noticed recurring implicit assumptions. The proposed solutions are designed for a world where Internet access and smartphone ownership are a given, people are willing and able to install these apps, and those who receive notifications about potential exposure to the virus have access to testing and can isolate safely. In this work we challenge these assumptions. We not only show that there are not enough smartphones worldwide to reach required adoption thresholds but also highlight a broad lack of internet access, which affects certain groups more: the elderly, those with lower incomes, and those with limited ability to socially distance. Unfortunately, these are also the groups that are at the highest risks from COVID-19. We also report that the contact tracing apps that are already deployed on an opt-in basis show disappointing adoption levels. We warn about the potential consequences of over-extending the existing state and corporate surveillance powers. Finally, we describe a multitude of scenarios where contact tracing apps will not help regardless of access or policy. In this work we call for a comprehensive and equitable policy response that prioritizes the needs of the most vulnerable, protects human rights, and considers long term impact instead of focusing on technology-first fixes.