Recent advances in GenAI have enabled automation in data visualization, allowing users to generate visual representations using natural language. However, existing systems primarily focus on automation, overlooking users' varying expertise levels and analytical needs. In this position paper, we advocate for a shift toward adaptive GenAI-driven visualization tools that tailor interactions, reasoning, and visualizations to individual users. We first review existing automation-focused approaches and highlight their limitations. We then introduce methods for assessing user expertise, as well as key open challenges and research questions that must be addressed to allow for an adaptive approach. Finally, we present our vision for a user-centered system that leverages GenAI not only for automation but as an intelligent collaborator in visual data exploration. Our perspective contributes to the broader discussion on designing GenAI-based systems that enhance human cognition by dynamically adapting to the user, ultimately advancing toward systems that promote augmented cognition.