Variational phase-field models have developed into powerful tools for simulating crack initiation and propagation, providing both a rigorous energetic structure and seamless handling of complex crack topologies. However, recent work has highlighted that while classical formulations can model nucleation according to a strength surface, the specific form of this surface is implicitly predetermined by relationships between the model components, namely the crack density function, energy degradation function, regularization parameter, and elastic energy splitting scheme. Consequently, the incorporation of arbitrary strength surfaces into classical variational formulations is widely regarded as unachievable. In this contribution, we explore an approach for integrating general strength surfaces into variational phase-field formulations for fracture while preserving energetic consistency. In particular, we retain the classical feature whereby the phase field directly degrades the elastic strain energy density. Our starting hypothesis is that crack nucleation is inherently statistical in nature, driven by randomly distributed microstructural flaws, even though it is commonly modeled using deterministic strength criteria at the continuum scale. Accordingly, nucleation should be treated as conceptually independent from the energy-based mechanisms governing subsequent Griffith-type crack extension. In this context, variational phase-field models that exhibit a well-defined elastic regime prior to damage evolution provide a suitable steppingstone. Such formulations allow for a clear separation between elastic response, strength-controlled nucleation, and energy-driven crack growth. Within this setting, we examine how a strength surface may be introduced into the bulk energy term of the total energy functional without altering the fundamental variational structure of the model, such that the governing equations for stress equilibrium and damage evolution arise naturally from variational derivatives of the total energy. Furthermore, we aim to decouple the strength surface from the elastic energy splitting scheme, allowing the latter to be designed solely for its primary purpose of modeling unilateral contact behavior between crack surfaces.