Artificial intelligence (AI) systems increasingly achieve expert-level predictive accuracy in healthcare, yet improvements in model performance often fail to produce corresponding gains in patient outcomes. We term this disconnect the allocation gap and provide a decision-theoretic explanation by modelling healthcare delivery as a stochastic allocation problem under binding resource constraints. In this framework, AI acts as decision infrastructure that estimates utility rather than making autonomous decisions. Using constrained optimisation and Markov decision processes, we show how improved estimation affects optimal allocation under scarcity. A synthetic triage simulation demonstrates that allocation-aware policies substantially outperform risk-threshold approaches in realised utility, even with identical predictive accuracy. The framework provides a principled basis for evaluating and deploying healthcare AI in resource-constrained settings.