Large language model-based web agents have demonstrated strong performance on realistic web interaction tasks. However, existing evaluations are predominantly conducted under relatively stable and well-behaved interaction conditions, which may overestimate agent robustness. High task success in such idealized settings does not necessarily reflect performance under realistic web interaction. To address this limitation, we introduce a diagnostic stress-testing benchmark for web agents. We first construct realistic and controllable web environments that provide clean and stable interaction workflows as reference baselines. We then introduce structured and controlled perturbations that emulate interaction variability, including shifting layouts, altered interaction semantics, and execution disruptions. By comparing agent behavior between clean and perturbed settings, our framework enables systematic diagnosis of robustness under what-if interaction scenarios. Through extensive evaluation of state-of-the-art multimodal web agents, we show that stress-based evaluation exposes failure modes and substantial robustness gaps that remain hidden under clean benchmark conditions.