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Materials informatics has achieved rapid progress in predicting composition–structure–property relationships, enabling accelerated screening, surrogate modeling, and exploration of high-dimensional design spaces. However, much of this success remains structurally grounded in correlational learning rather than in explanatory, transportable, or intervention-relevant forms of understanding. This conceptual manuscript argues that correlation-centric models, while often sufficient for ranking candidates under training-like conditions, are epistemically underpowered for high-stakes materials decisions such as processing optimization, microstructural control, deployment certification, and failure-sensitive design, where actions must remain defensible under distribution shift, partial observability, and changing constraints. In such settings, predictive accuracy alone does not establish decision legitimacy: a model may be correct for reasons that do not remain stable under deliberate intervention, confounding, or selection effects, thereby producing actionable recommendations without causal warrant. Motivated by recent developments in structural causal models, causal discovery, counterfactual inference, and invariant representation learning, this paper advances a theory-first reframing: materials AI should be treated as an epistemic instrument whose outputs must be qualified by the causal status they can legitimately support. We propose a novel framework—the Causal Warrant Ladder (CWL)—that classifies materials-model outputs into five ascending levels of causal legitimacy: associative regularities, transportable relations, mechanistic constraints, interventional guidance, and counterfactual design claims. CWL is paired with a Causal-Readiness Map, which specifies the minimal conceptual conditions required for upward movement on the ladder, including identifiability assumptions, invariance structure, intervention semantics, and decision stakes. By separating predictive competence from causal legitimacy, this roadmap provides a disciplined conceptual pathway beyond “black-box correlation” toward materials reasoning that supports robust and responsible design action.