I wholeheartedly agree, but that is not how the mapping community ticks like. Mapping a separate sidewalk indeed turns the “highway” into a “carriageway” instead. From my point of view nothing makes the “sidewalk” less capable of bearing the the name of the street. After all, historically they were the first to receive Pavement 
So mapping a separate sidewalk and not adjusting the “highway” to say, that it maps a carriageway only, indeed impairs data usability.
PS: 1) I consider “foot=no” on the highway/carriageway a bad manoeuvre (seen that, to force routers to use the separately mapped footway.) 2) There may be better keys to record the name of the street to use on a sidewalk than “name”. Could this be applied to “carriageways” just the same?