Exactly. The HTTP standard doesn't really mention HTML, except tangentially in examples. And regarding cookies, there are even people who use cookies in RPC contexts, but this is rather rare, and as you said, entirely optional.
Also, as a minor point, even when browsing the web, a minority of the actual requests deliver HTML -- most of them are for various kinds of media referenced by the HTML document.
There are a few bits that don't make sense eg cookies where the server sends something and the client is expected to remember it but they can just be ignored.