I am looking at HTTP Cache Control Mechanism, and have a question on cache-control: private.

Here is the W3C specification on private cache control.

private

Indicates that all or part of the response message is intended for a single user and MUST NOT be cached by a shared cache. This allows an origin server to state that the specified parts of the response are intended for only one user and are not a valid response for requests by other users. A private (non-shared) cache MAY cache the response. Note: This usage of the word private only controls where the response may be cached, and cannot ensure the privacy of the message content.

Source: https://www.w3.org/Protocols/rfc2616/rfc2616-sec14.html#sec14.9.1

which seems to disable caching on all the servers in the middle, e.g. by ISP Server. However, as we all know that HTTPS have encrypted its content, path and even header, So intermediate servers should not be able to cache the content meaningfully.

So is there any real usage / difference when I add cache-control: private to Https Header? Or will the browser or any Https client when visit the same page have any different behavior? Will there be any edge cases where having cache-control: private to a Https request does make a difference?

I know for sure cache-control: private is useful in Http, but is it useful in Https?