Software frameworks are intended to accelerate development by providing pre-built structures and abstractions. However, this convenience is not without cost: these structures invariably introduce a measurable and often excessive structural overhead. This paper introduces the Accidental Complexity Score (ACS), a novel and reproducible metric designed to quantify this precise architectural burden. ACS operates by measuring the volume of primary structural components such as classes, interfaces, traits, and user-defined functions, that must be loaded during the minimal execution of an application. Using a minimal "Hello World" implementation, six popular PHP frameworks are evaluated to isolate and compare their intrinsic structural complexity. The results reveal substantial variation: lightweight frameworks maintain minimal overhead, while heavily structured architectures exhibit a high structural cost that demonstrably correlates with increased memory consumption and execution time. The ACS is framed as a clear measure of Architectural Complexity (AC) relative to an Optimal Algorithmic Implementation (OAI). These findings provide developers and system architects with actionable, empirical data for selecting frameworks, allowing them to make informed trade-offs between architectural richness and essential performance efficiency. This work establishes a foundation for future research aimed at minimizing structural overhead in software systems.