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Artificial intelligence (AI) is increasingly positioned as a design partner in materials optimization, enabling accelerated exploration of vast composition–processing–structure spaces under multiple, often conflicting, targets. Yet sustainability-centered materials design is not simply a larger version of multi-property optimization: it requires negotiating trade-offs across heterogeneous objective types such as performance, cost, safety, emissions, toxicity, circularity, and resource criticality, while accounting for lifecycle shifts and stakeholder-dependent priorities. Many current AI-enabled optimization workflows implicitly treat trade-offs as static Pareto-front problems with stable objective meanings and fixed feasibility boundaries. This conceptual manuscript argues that such assumptions are structurally incompatible with sustainable materials decisions, which involve trade-offs that are contextual, value-weighted, and regime-dependent. We introduce a novel theoretical framework—Trade-Off Sensitivity Theory (TOST)—which models sustainability optimization as a decision process governed by objective incompatibility geometry, lifecycle constraint migration, uncertainty-to-consequence coupling, and preference volatility. Rather than proposing algorithms or empirical evaluation, TOST provides a theoretical map linking Pareto efficiency to sustainability legitimacy through three layers: objective semantics, trade-off sensitivity, and action admissibility. The framework clarifies when AI outputs support responsible selection, when optimization is ill-posed, and how sustainable decisions can be justified under conflicting criteria.