With the approval of the crossing:markings=* proposal there is now a satisfactory way of tagging whether a crossing is marked or not regardless of the crossing being uncontrolled or having traffic signals. For signals, there is crossing:signals=* which fulfills the same role but has not been formally approved yet.
As such, I propose to approve crossing:signals=* and additionally deprecate crossing=* (except crossing=no).
Please sound off your feedback and comments here, the corresponding mailing list or on the wiki talk page.
I am aware and my intention was to propose both together. I have discussed the similar proposal you linked and will support approving that one should this one fail. The latter one doesn’t include the deprecation of crossing=*.
Have you already had contact with data consumers about this? When deprecating such a common Key (7 million uses) I think your proposal should have a more detailed migration plan.
There should also be a clear plan for updating editors (iD, StreetComplete, etc).
iD was recently updated to include support for crossing:markings=* but in doing so changed crossing=marked to crossing=uncontrolled for its “Marked Crosswalk” preset and will likely need to be updated again pending another change to crossing. Current discussion