Website Fingerprinting (WFP) uses deep learning models to classify encrypted network traffic to infer visited websites. While historically effective, prior methods fail to generalize to modern web environments. Single-page applications (SPAs) eliminate the paradigm of websites as sets of discrete pages, undermining page-based classification, and traffic from scripted browsers lacks the behavioral richness seen in real user sessions. Our study reveals that users exhibit highly diverse behaviors even on the same website, producing traffic patterns that vary significantly across individuals. This behavioral entropy makes WFP a harder problem than previously assumed and highlights the need for larger, more diverse, and representative datasets to achieve robust performance. To address this, we propose a new paradigm: we drop session-boundaries in favor of contiguous traffic segments and develop a scalable data generation pipeline using large language models (LLM) agents. These multi-agent systems coordinate decision-making and browser interaction to simulate realistic, persona-driven browsing behavior at 3--5x lower cost than human collection. We evaluate nine state-of-the-art WFP models on traffic from 20 modern websites browsed by 30 real users, and compare training performance across human, scripted, and LLM-generated datasets. All models achieve under 10\% accuracy when trained on scripted traffic and tested on human data. In contrast, LLM-generated traffic boosts accuracy into the 80\% range, demonstrating strong generalization to real-world traces. Our findings indicate that for modern WFP, model performance is increasingly bottlenecked by data quality, and that scalable, semantically grounded synthetic traffic is essential for capturing the complexity of real user behavior.