Most of the time when I do any further processing (save to file, pipe to other tools, etc) I'm interested in the response body. The headers are a useful diagnostic, and things like cookies are useful to save, but those don't typically belong in the same stream: I can't do the same things to the headers as I can the body, and so including both in the same stream will tend to reduce my options for downstream processing. If I actually do want them both in the same stream I can redirect stderr to stdout.