Data visualization amplifies cognition and broadens access to information. Yet most visualizations are designed with a narrow audience in mind, assuming users who are analytically driven, highly data-literate, and comfortable with abstraction. This approach excludes many, particularly those with cognitive disabilities, who may struggle with abstraction, experience sensory overload, or have limited exposure to statistical conventions. Working with individuals with Intellectual and Developmental Disabilities (IDD), my research reveals both the limitations and the untapped possibilities of visualization. Through graphical perception studies, interviews, and co-design, I examine how cognitively diverse individuals interpret visualizations, engage with data in daily life, and create more accessible data representations. These insights inform practical design guidelines while reimagining visualization as a medium for more accessible, expressive, and creative forms of data engagement. Building on this foundation, I outline a vision for a cognitively inclusive future of visualization, one that transforms how people experience, understand, and connect through data.