Although language model-based chat systems are increasingly used in daily life, most Americans remain non-adopters of chat-based LLMs -- as of June 2025, 66% had never used ChatGPT. At the same time, LLM development and evaluation rely mainly on data from adopters (e.g., logs, preference data), focusing on the needs and tasks for a limited demographic group of adopters in terms of geographic location, education, and gender. In this position paper, we argue that incorporating non-adopter perspectives is essential for developing broadly useful and capable LLMs. We contend that relying on methods that focus primarily on adopters will risk missing a range of tasks and needs prioritized by non-adopters, entrenching inequalities in who benefits from LLMs, and creating oversights in model development and evaluation. To illustrate this claim, we conduct case studies with non-adopters and show: how non-adopter needs diverge from those of current users, how non-adopter needs point us towards novel reasoning tasks, and how to systematically integrate non-adopter needs via human-centered methods.