The strong decay ψ(4040) → \( D\overline{D} \) is anomalously suppressed despite ample phase space, whereas the \( D{\overline{D}}^{\ast } \) and \( {D}_s{\overline{D}}_s \) channels remain sizable. In this work, we study this suppression and the associated open-charm hierarchy in the framework of the instantaneous Bethe-Salpeter equation combined with the relativistic 3P0 model, with the pair-creation strength fixed independently from ψ(3770) → \( D\overline{D} \) . Within this framework, we show that the suppressed \( D\overline{D} \) mode can be understood as a consequence of node-induced cancellations in the relativistic decay amplitude. The \( D\overline{D} \) amplitude is strongly reduced because the corresponding overlap integral receives comparable positive and negative contributions from different momentum regions, whereas the \( D{\overline{D}}^{\ast } \) and \( {D}_s{\overline{D}}_s \) channels do not undergo the same strong cancellation. This interpretation is further supported by the pronounced sensitivity of the \( D\overline{D} \) width to the initial mass, the charged-neutral D-meson mass splitting, and the dip structure in the mass dependence of the partial width. Our results provide a dynamical explanation of the suppressed \( D\overline{D} \) mode and the core open-charm hierarchy of ψ(4040) within a conventional 3 3S1 charmonium picture, while the precise value of the near-vanishing \( D\overline{D} \) width remains model dependent.
