No, you're talking about costs to user, which are oversimplifications of the costs that providers bear. One output token with a million input tokens is incredibly cheap for providers
Input tokens usually dominate output tokens by a lot more than 2x though. It’s often 10x or more input. It can even easily be 100x or more. Again in realistic workflows.
Caching does help the situation, but you always at least pay the initial cache write. And prompts need to be structured carefully to be cacheable. It’s not a free lunch.
Source? Afaik this is incorrect.