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Graph neural networks (GNNs) for crystalline materials are typically constructed with finite cutoff radii of approximately 5–6 Å, constraining message passing to local atomic environments. While this design ensures computational tractability and captures short-range interactions characteristic of covalent, metallic, and van der Waals systems, it systematically excludes long-range electrostatic contributions that govern the behavior of polar crystals. In ferroelectrics, piezoelectrics, and related perovskite oxides, Coulomb interactions decay as 1/r and accumulate over extended length scales, such that each ion experiences a lattice-wide electrostatic field. Truncation at the graph level therefore induces structural rather than incremental error, yielding suppressed dielectric responses, elimination of ferroelectric instabilities, collapse of LO–TO phonon splitting, vanishing domain-wall energies, and incorrect surface reconstructions. Empirical studies confirm that these discrepancies persist even in data-rich regimes and are not resolved by equivariant architectures, which retain the same locality constraint. This work interprets these failures as deterministic consequences of an incompatible inductive bias, rather than as limitations of training data or optimization. By formalizing recurrent failure modes and linking them to the underlying electrostatic omission, the analysis reframes polar crystals as a critical stress test for graph-based models. Physically grounded remedies—including Ewald-consistent objectives, multipole representations, hybrid local–global architectures, and self-consistent charge equilibration—demonstrate that long-range interactions can be incorporated without sacrificing scalability. The central implication is that locality, as currently encoded in crystal GNNs, is not a universally valid assumption but a regime-dependent approximation whose breakdown is most acute in precisely those materials where predictive fidelity is technologically consequential.