Basic JSON Schema is for describing data structures in general. As such, it is great for validating HTTP request and response bodies. It is not particularly capable of describing the rich fullness of HTTP requests.
The hyperschema spec partially bridges that gap by offering media types and named hrefs. But there's a lot more to HTTP than URLs and media types. Standardized HTTP headers vary wildly in their formats and uses. Custom headers may use whatever format the developer desires. I do not think JSON Schema should even try to handle this problem. Schemas are useful for validating or reflecting on data structures.
What I suspect you're looking for (because I've been trying to solve this problem for years) is a format for describing HTTP APIs that is as useful as JSON Schema. Such a forrmat would also be an excellent basis for auto-generation of documentation. Ideally, we could describe an HTTP API in a form that could be serialized to JSON, and both server and clients could make use of the description.