It's not about "constructing a prompt" in the sense of building the prompt string. That of course wouldn't be costly.
It is about reusing llm inference state already in GPU memory (for the older part of the prompt that remains the same) instead of rerunning the prompt and rebuilding those attention tensors from scratch.
that is what caching is doing. the llm inference state is being reused. (attention vectors is internal artefact in this level of abstraction, effectively at this level of abstraction its a the prompt).
The part of the prompt that has already been inferred no longer needs to be a part of the input, to be replaced by the inference subset. And none of this is tokens.
I think you missed what the parent meant then, and the confusing way you replied seemed to imply that they're not doing inference caching (the opposite of what you wanted to mean).
The parent didn't said that caching is needed to merely avoid reconstructing the prompt as string. He just takes that for granted that it means inference caching, to avoid starting the session totally new. That's how I read "from prompting with the entire context every time" (not the mere string).
So when you answered as if they're wrong, and wrote "constructing a prompt shouldn't be same charge/cost as llm pass", you seemed to imply "constructing a prompt shouldn't be same charge/cost as llm pass [but due to bad implementation or overcharging it is]".