WebGPU's security-focused design imposes per-operation validation that compounds across the many small dispatches in neural network inference, yet the true cost of this overhead is poorly characterized. We present a systematic characterization of WebGPU dispatch overhead for LLM inference at batch size 1, spanning four GPU vendors (NVIDIA, AMD, Apple, Intel), two native implementations (Dawn, wgpu-native) and three browsers (Chrome, Safari, Firefox), and two model sizes (Qwen2.5-0.5B and 1.5B). Our primary contribution is a sequential-dispatch methodology that reveals naive single-operation benchmarks overestimate dispatch cost by ${\sim}20\times$. The true per-dispatch cost of WebGPU API overhead alone is 24-36 $μ$s on Vulkan and 32-71 $μ$s on Metal, while the total per-operation overhead including Python cost is ${\sim}95$~$μ$s, which turns out to be a distinction critical for optimization. On Vulkan, kernel fusion improves throughput by 53%, while CUDA fusion provides no benefit, confirming that per-operation overhead is a primary differentiator. LLM inference was tested across three major operating systems (Linux, Windows, macOS). We built $\texttt{torch-webgpu}$, a PrivateUse1-based out-of-tree PyTorch backend and an FX-to-WebGPU compiler, which on our reference platform achieves 11--12% of CUDA performance. At dtype-matched float32, RTX PRO 2000 achieves 1.4$\times$ WebGPU's throughput despite ${\sim}6\times$ less compute than RTX 5090. For dispatch overhead, backend choice is the dominant factor, although implementation choice also matters substantially within a backend (2.2$\times$ for Metal). In terms of dispatch vs kernel compute efficiency, we conclude that at batch=1 with the current dispatch-heavy pipeline, per-operation overhead dominates regardless of kernel quality. All code, benchmarks, and raw data are open source.