Why does the system work like that? Is the cache local, or on Claude's servers?
Why not store the prompt cache to disk when it goes cold for a certain period of time, and then when a long-lived, cold conversation gets re-initiated, you can re-hydrate the cache from disk. Purge the cached prompts from disk after X days of inactivity, and tell users they cannot resume conversations over X days without burning budget.
The cache is on Antropics server, its like a freeze frame of the LLM inner workings at the time. the LLM can pick up directly from this save state. as you can guess this save state has bits of the underlying model, their secret sauce. so it cannot be saved locally...