I share your dislike, but I wasn't aware the phenomenon was a true Americanism (in the way that 'color', 'plow' etc. are). It always jars with me when I read US newspaper headlines that do this, but then I've noticed the same in older (e.g. WW2-era) British papers. Is this one of those things, like some aspects of punctuation, where British usage has evolved further from traditional usage than US has?
I would say that it is, but at the same time US usage is not uniform. The New York Times
(which is conservative in other ways--e.g. the use of courtesy titles like "Mr." and "Ms." when referring to specific people in articles, which nowadays seems almost patronizing) and the Washington Post
both use initial caps in headlines, but the Wichita Eagle
uses sentence case, much like the Guardian
in the UK.
Where UK traffic signing is concerned, the big sea change came with Anderson and, to a much greater extent, Worboys. It was David Kindersley who lost the battle for all-caps on traffic signs in the early 1960's. In contradistinction, the US signing system is a more or less seamless continuation (bar the introduction of rounded typefaces in 1945, green background for guide signs in 1958-1971, and symbol signs in 1971) of that spelled out in the AASHO signing and marking manual for US highways in 1927.