If we deprecate crossing we would be going against all the conventions that have already been established elsewhere in the tagging, for example we don't describe sidewalks as a set of properties added to ways with the tag highway=footway, we add footway=sidewalk to describe that something is a sidewalk. by the same logic we shouldn't describe different types of crossings with different tagging, we should just say the type of crossing through a crossing tag. in the same way as footway=* tells you the type of footway crossing=* tells you the type of crossing.
∴ if we deprecate crossing=* we should also by the same logic deprecate footway=* since they both serve the same purpose in specifying the type that they are.

I'll add a note here that there are really ony two types of crossings, uncotrolled and controlled(traffic_signals), I agree that the tagging still needs some work, I just think that we should deprecate crossing=unmarked as we did with crossing=marked since crossing=unmarked and crossings:markings=no encode the same information and since they are duplicate information one should be removed. Due to the fact that crossing=uncotroled and traffic_signals (what I'm calling controlled) do not encode the type of marking present at a crossing, crossing:markings=* is neccessary for cases were crossinga:markings is not "no" and ∴ crossings=unamrked should be deprecated. this does not apply to crossing:signals=* since if crossing=unmarked is deprecated then the two values of crossing=* would already encode the same infomation as crossings:signals=* and since crossings=* already exists we dont need a new tag and ∴ crossings:signals=* should be depredcated. essentially we either deprecate crossing:markings or crossings:signals and since it is significantly harder (it takes exponetially more tags) to encode crossings:markings fully into crossings=* it should be the one thats kept since all it takes to encode the same information as crossing:signals into crossing=* is two tags that we already have. 

Happy mapping,
Udar.