To extend your point: it's not really the storage costs of the size of the cache that's the issue (server-side SSD storage of a few GB isn't expensive), it's the fact that all that data must be moved quickly onto a GPU in a system in which the main constraint is precisely GPU memory bandwidth. That is ultimately the main cost of the cache. If the only cost was keeping a few 10s of GB sitting around on their servers, Anthropic wouldn't need to charge nearly as much as they do for it.
That cost that you're talking about doesn't change based on how long the session is idle. No matter what happens they're storing that state and bring it back at some point, the only difference is how long it's stored out of GPU between requests.