This paper develops a general theory explaining why centralized institutions stagnate, consolidate, or collapse even in the absence of scarcity, corruption, or malicious intent. Beginning with archaeological inference from Göbekli Tepe, the study formalizes a structural failure mode termed the productivity–visibility paradox, in which increasing visibility of productive output leads to escalating downside variance through discretionary or algorithmic extraction. Rational agents respond by suppressing output and reallocating effort toward political or compliance activity, producing institutional decay. The model is generalized mathematically and applied to modern systems including taxation and healthcare billing, where it quantitatively predicts forced consolidation as a variance-minimization strategy. The paper demonstrates that consolidation, stagnation, and burnout arise from unbounded downside risk rather than market power or ideology. Finally, the model is unified with findings from generative systems theory, showing that development requires bounded error while extractive systems amplify variance and arrest growth. All mathematical examples are illustrative and intended to demonstrate structural incentives rather than precise empirical calibration.