Demographic projections feed directly into some of the highest-stakes risk-management decisions governments make, from pension system solvency to labour-force and fiscal-sustainability planning, yet the uncertainty surrounding these projections is rarely subjected to the kind of structured uncertainty and sensitivity analysis routine in other risk-modelling domains. We examine two case studies that illustrate the resulting risk. The first is a retrospective model-validation exercise on the optimisation-based population model of Song et al., which underpinned China’s one-child policy: applying global uncertainty analysis reveals that the model is, by construction, insensitive to demographic inputs and converges to its predetermined target population of approximately 700 million regardless of parameter variation—a textbook case of a model that obscures rather than informs the risk it claims to manage. The second is a modelling-of-the-modelling-process experiment projecting global population to 2050 and 2075 across seven configurations spanning three projection paradigms (Cohort-Component, Lotka intrinsic growth rate, and ARIMA) and two intra-paradigm sub-model choices, with ten uncertain inputs and 22,528 Sobol’ model evaluations. The choice of projection paradigm alone accounts for 87–90% of output variance, dwarfing all parametric uncertainty combined; intra-paradigm sub-model choices contribute a further 2–5%. We show that current policy-relevant demographic inputs—including the European Commission’s 2024 Ageing Report and an IMF Staff Discussion Note on pension systemdesign—rely on single demographic models with no structural uncertainty quantification, leaving a substantial, unrecognised source of model risk embedded in fiscal and pension policy. We conclude with concrete, transferable heuristics for distinguishing genuine decision-support models from models that function as advocacy instruments wrapped in mathematical form, of direct relevance to risk analysts validating models in any domain where structural model choice, not just parametric uncertainty, drives decision-relevant variance.