Since the start of the Covid-19 pandemic in early 2020, conspiracy theories, misinformation, and fake news about the virus have abounded, drastically affecting global health measures to oppose it. In response, different strategies have been proposed to combat such Covid-19 collective irrationalities. One suggested approach has been that of epistemic paternalism – non-consultative interference in agents’ inquiries for their epistemic improvement. While extant literature on epistemic paternalism has mainly discussed whether it is (ever) justified, in this paper, I primarily focus on the potential implementation of widespread epistemically paternalistic policies (such as no-platforming and censorship) and its consequences. I argue that pursuing epistemic paternalism to combat Covid-19 collective irrationalities leads to a hitherto unnoticed puzzle for proponents of epistemic paternalism. Central to the puzzle is the idea those (governments, corporations, social media giants) who actually can (i.e., have the requisite power to) enact widespread epistemically paternalistic policies seem the institutions who are least suited to having such informational control over the populace. Thus, epistemic paternalism appears a sword without a hilt; while it may prove an effective strategy in tackling Covid-19 collective irrationalities, we do not have any way to use it without incurring serious risks.