I think (without any kind of supporting evidence) that git chose to use terse diffs so they could be emailed to mailing lists. Git's diffs aren't backwards compatible with patch by default; I'm not sure that was the reason. All of that is to say: I think there are reasons why a modern patch format might reasonably choose terseness.

(Personally, I would just push for request body compression. It's not common but it's not impossible, and then you get the best of both worlds. I bet the terse format compresses to roughly the same size as the verbose format.)