so then logically we should also remove footway=* tags. that's the pattern here, you have a tag telling you what the feature is and then then a tag that starts with what it is from the previous tag telling you what type of what it is it is.
for example sidewalks, highway=footway tells you they are a footway but since sidewalks a re more specific than the nebulous "footway" you specify the type of footway with footway=sidewalk. the same logic applies for crossings. highway=footway tells you they are pedestrian navigation features, footway=crossings tells you that the feature is for crossings roads but that isn't all the information that matters about a crossings, you also have to know whether or not its signalized since that is what distinguishes crossings, not how they are marked so you need a crossings=*. 
As I clearly laid out in the above post (see it for more detail) this makes crossings:signals=* the imposter here and thus it should be deprecated.

just because the tag crossings=* has in the passed been inconsistently interpreted in the passed doesn't mean it has to now. the change is rather simple in fact, all we have to do is deprecate all crossings=* values other than uncontrolled and traffic_signals (as laid out above); and although that change would make it abundantly clear what the meaning of crossings=* is we specify in the wiki that it is purely for whether or not it is signalized. that is anyways basically the state of things now. again all we have to do is deprecate all 910 other tags apparently.

again, as to keep the tagging internally consistent either we deprecate crossing:signals or  both crossings=* and footway=*. pick your poison apparently.

Happy mapping,
Udar.