HTML observations in LLM-based web agents are extremely long, and while many reduction methods have been proposed, it remains unclear which methods reduce overall agent latency while maintaining performance. The main obstacle is the high cost of end-to-end evaluation: in our experiments, evaluating 11 methods across 32 configurations on 33 tasks of WorkArena L1 required 232.4 cumulative hours. To address this, we propose a lightweight evaluation framework based on the Minimal Failure Set (MFS), the minimal set of HTML elements whose removal causes task failure. We define coverage as the fraction of instances in which a reduction method fully retains the MFS, which serves as a proxy metric that requires neither web access nor LLM inference. We validate that coverage strongly correlates with end-to-end success rate, with over 100$\times$ speedup in cumulative evaluation time on both benchmarks. Using this framework, we find that extractive HTML reduction methods require either high computation cost or domain-specific optimization to reduce agent latency while maintaining performance. Building on this, we optimize a pruning program on MFS training data, achieving 2.2$\times$ faster per-step latency on WorkArena L1 while retaining 84\% of the original success rate, and 3.1$\times$ faster on WebLinx while retaining 89\%.