Users demand fast, seamless webpage experiences, yet developers often struggle to meet these expectations within tight constraints. Performance optimization, while critical, is a time-consuming and often manual process. One of the most complex tasks in this domain is modifying the Document Object Model (DOM), which is why this study focuses on it. Recent advances in Large Language Models (LLMs) offer a promising avenue to automate this complex task, potentially transforming how developers address web performance issues. This study evaluates the effectiveness of nine state-of-the-art LLMs for automated web performance issue resolution. For this purpose, we first extracted the DOM trees of 15 popular webpages (e.g., Facebook), and then we used Lighthouse to retrieve their performance audit reports. Subsequently, we passed the extracted DOM trees and corresponding audits to each model for resolution. Our study considers 7 unique audit categories, revealing that LLMs universally excel at SEO & Accessibility issues. However, their efficacy in performance-critical DOM manipulations is mixed. While high-performing models like GPT-4.1 delivered significant reductions in areas like \textit{Initial Load}, \textit{Interactivity}, and \textit{Network Optimization} (e.g., 46.52% to 48.68% audit incidence reductions), others, such as GPT-4o-mini, notably underperformed, consistently. A further analysis of these modifications showed a predominant additive strategy and frequent positional changes, alongside regressions particularly impacting \textit{Visual Stability}. Our findings define safe areas for automation (e.g., SEO and accessibility) and reveal the limits of DOM-level resolution, underscoring the need for hybrid, validated workflows. However, it critically underscores the need for careful model selection, understanding their specific modification patterns, and robust human oversight to ensure reliable web performance improvements.