Despite decades of development efforts, 1.1 billion people remain multidimensionally poor. This paper argues that persistent poverty is not merely a resource problem but a systemic design failure in the structure of accountability within governance architectures. Through a qualitative multi-method approach that combines comparative case studies, a systematic literature review, and legal-normative analysis, the study examines how accountability design features shape multidimensional poverty outcomes. The analysis reveals that even well-resourced programmes fail when eligibility rules are opaque, grievance systems are inaccessible, and wrongful exclusion cannot be effectively contested. Conversely, resource-constrained programmes succeed when accountability is intentionally designed. The paper proposes three legal-institutional innovations to address identified failure modes: a Protocol to the International Covenant on Economic, Social and Cultural Rights; a Poverty-Climate Fund window; and a feasible international adjudication pathway. The paper concludes that eradicating multidimensional poverty requires reconceptualising it as a justice imperative and a design challenge.