As large language models (LLMs) continue to grow in scope and capability, privacy concerns are on the rise. Since users increasingly interact with a single general-purpose system across many distinct contexts, there is a natural tendency to pursue a one-size-fits-all solution to privacy. Unfortunately, this overlooks a crucial insight from decades of privacy research: privacy is inherently contextual. In this paper, we argue that existing work in prompt privacy is drifting towards attempts to design a unified framework, which is highly misleading and can foster a false sense of security. Furthermore, we argue that even future work in this direction needs to wrestle with fundamental tensions across various desirable properties of prompt privacy. Thus, such continued attempts towards a unified framework need to be reconsidered. We recommend three critical paths forward: application-specific deployment of LLMs, context-specific evaluation of privacy frameworks, and better privacy literacy.

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