The coupled criterion [1] has proved to be an efficient method to study brittle crack initiation in various configurations [2]. Despite its strong potential for understanding the mechanisms behind crack initiation, the Coupled Criterion (CC) still presents limitations in certain pathological configurations where it fails to provide a complete failure description. Specifically, the CC proves inadequate in cases where the energy criterion dominates over the stress criterion. In such scenarios, no characteristic length naturally emerges from the interaction between strength and energy considerations, as this coupling is effectively "disabled," reducing the CC to a purely energy-based criterion. Consequently, the initiation load predicted by the CC becomes independent of tensile strength, particularly in cases involving strong singularities or the propagation of semi-infinite cracks under remote anti-plane shear loading. The key missing element in these configurations is the representation of a process zone preceding crack initiation. In this work, we demonstrate how integrating a process zone into the Coupled Criterion—through regularization via phase-field models and matched asymptotic expansions—enhances its predictive capabilities.