One could argue that the headers comprise a very important 0.1%, but any wasted time the client spends waiting for and parsing headers will almost always be utt

One could argue that the headers comprise a very important 0.1%, but any wasted time the client spends waiting for and parsing headers will almost always be utterly dominated by the unavoidable wait for HTML parsing, JavaScript parsing, painting and so on. I could see the argument for pruning useless headers if, say, the method for generating them relied on some high-latency database call or filesystem access, but that would rarely be the case.