Data visualization aims to augment human cognition and make data accessible to diverse audiences. As data increasingly shapes participation and decision-making across many domains, there is a growing need to examine whether prevailing assumptions in visualization adequately reflect the diversity of human abilities, experiences, and needs. We argue that cognitive accessibility provides a critical lens for examining these questions and functions as a stress test for visualization theory. Drawing on cognitive accessibility research and our experiences studying accessible visualization, we identify three interconnected assumptions that shape visualization research and practice: assumptions about what forms of cognition visualization supports, how accessibility is defined and measured, and whose needs and abilities are centered in design and evaluation. Making these assumptions explicit reveals opportunities to rethink longstanding approaches and open new directions. Ultimately, we believe that cognitive accessibility can serve as a catalyst for innovation, expanding what visualization supports, whom it serves, and the roles it plays in people's lives.

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