This paper examines how social media platforms - as a new form of media organization - challenge the principles of a democratic public sphere, a key pillar of liberal-democratic societies. To do so, we draw on the institutional logics perspective, which allows connecting societal-level institutional orders with the ways in which organizations, sometimes strategically, use and thereby potentially redefine these orders. Based on comprehensive secondary data, we analyze YouTube as an exemplary case of how the logics of the market, the corporation, and the community are selectively appropriated and strategically subverted by large, centralized and commercially oriented social media platforms. YouTube rhetorically deploys market logic narratives of meritocratic competition and equal opportunity, yet operationally creates algorithmic hierarchies that favor established creators and concentrate market power. Similarly, the platform invokes the community logic by promoting democratic participation and collective expression while its algorithmic architecture amplifies polarizing content and fragments public discourse. The corporate logic manifests through bureaucratic governance structures that extend organizational control to users without reciprocal accountability mechanisms. Examining the Fediverse as an organizational alternative based on decentralized architectures and distributed governance, we argue that these mechanisms reflect strategic choices rather than technological inevitability. Highlighting the power of social media platforms to manipulate and undermine institutional logics, we discuss how contestation around their governance also entails contestation around the interinstitutional system structuring societies because of their important role in shaping the public sphere.