OSM prefers British spelling, but imo should not necessarily prefer British terms if there are other factors to consider. In this case, “pavement” could be mistaken for one of the other, less common meanings of the word which are also related to construction and roads: http://en.wikipedia.org/wiki/Pavement

Not only are there very few existing uses of “pavement” as a key, but values like “asphalt” and “gravel” indicate that this confusion is actually taking place: http://taginfo.openstreetmap.org:8001/keys/pavement#values

So “sidewalk” does appear to be less potentially confusing and maybe a bit easier to understand for non-native speakers. I’m not sure whether that’s a strong enough argument to go for the American term, but let’s face it - that decision has already been made: You cannot really replace a tag that has 114 000 uses with a tag that has 600 without very good reasons.