Lawful exceptional access (EA) systems hold the cryptographic keys that decrypt protected communications for authorised parties. The debate over their risks has been long and qualitative, complicated by two problems: no public dataset of EA-specific compromise events exists, so assessment must use sparse, indirect evidence; and prior work has treated structurally different designs as equivalent, though transmission-layer EA in carrier infrastructure (T-EA) and over-the-top EA at the platform layer (OTT-EA) differ in how cryptographic keys relate to ciphertext data. This paper builds a structured uncertainty framework for evaluating systemic compromise risk in EA architectures. It does not produce predictive forecasts, which the evidence cannot support; it separates findings robust to assumptions from those that depend on calibration. Four analytical layers are applied to T-EA and OTT-EA: three empirical pillars (historical analogues, a Monte Carlo scenario layer, a channel-independence decomposition) plus a Bayesian Structural Risk Model on a parallel-subgraph attack graph. The central findings are structural. First, EA-equipped architectures of either class carry strictly higher modelled risk than their no-EA counterfactual, an ordering independent of calibration. Second, the classes differ in distribution shape: T-EA risk is dominated by central tendency, OTT-EA by the tail under correlated campaigns. Third, calibration-conditional annual probability ranges span 1.4% to 12.9% for T-EA across the structured-judgement targeting-premium interval. Over multi-decade horizons, cumulative compromise is well above zero; key-material exfiltration is irreversible, weighing heavily on OTT-EA's larger user populations. The framework quantifies compromise probability, not expected harm; consequence modelling and benefit estimation are outside its scope.

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