This paper addresses the accessibility challenges of AI website builders for blind and low vision (BLV) users, focusing on how current tools fail to meet Web Content Accessibility Guidelines. We conducted expert user testing of three popular AI website builders—Dorik, Relume, and Wix—with a screen reader, finding significant accessibility barriers for BLV users. To mitigate these shortcomings, we propose integrating large language models (LLM) as AI assistants in website builders. These AI assistants would work collaboratively with BLV users to describe visual elements, assist in layout decisions, and perform actions that are currently inaccessible due to their reliance on mouse interactions. The contributions of this paper include a critique of current AI website builders, the concept of an assistant-based LLM model for improving the accessibility of builder platforms, and an explanation of an LLM-supported workflow for BLV users to design websites. Besides benefiting BLV website builder users, our design concept would enhance the overall accessibility of AI-generated websites.