Human cognitive bandwidth is a finite biological resource, yet modern administrative systems routinely assume its abundance. Drawing on Cognitive Load Theory, scarcity research, and the administrative burden framework, this paper argues that bureaucratic friction functions as a regressive cognitive tax: it systematically externalizes interpretation, coordination, and compliance costs onto individuals whose working memory is already constrained by stress, poverty, and the fragmentation of digital life. The paper maps learning, compliance, and psychological costs (Herd & Moynihan) onto intrinsic, extraneous, and stress-induced cognitive interference (Sweller; Mullainathan & Shafir), generating a falsifiable framework for analyzing how administrative systems produce predictable exclusion. Through cross-domain analysis (healthcare, immigration, taxation, voting, and platform labor), the paper proposes a new paradigm: cognitive infrastructure-systems designed to absorb bureaucratic complexity upstream before it reaches the user. It introduces "cognitive cost per citizen" as a measurable performance metric and outlines a research agenda for empirical validation. Administrative burden is treated as one important institutional vector of cognitive overload among many; the paper does not exhaust all sources of cognitive depletion in modern life. The central claim is not that bureaucracy should disappear, but that democratic legitimacy increasingly depends on whether institutions respect the finite architecture of the human mind.