I was under the impression that the cache write fee was added to both the input and output costs (except in cases where the cache write is explicitly disabled via e.g. DISABLE_PROMPT_CACHING). The output becomes part of the context, after all; if they don't (for some reason, due to disaggregated inference perhaps) then I'd expect output tokens get charged both output then input+cache_write on the subsequent completion request.

The pricing model confuses me though (I presume by design, Hanlon be damned).

You don't have to pay for cache write if prompt isn't part of conversation.