Interesting. I can definitely see the appeal of tagging as area:highway=crossing; however, area:highway=X has typically been used to provide the “width” of a linear highway=X that already has its own “length”.
In the case of a highway=crossing node, I’m not sure the scheme would extend logically in the same way, as the node has no length and no direction; I would instead consider the area:highway=* for the crosswalk as providing the “width” of the highway=footway+footway=crossing way (which I’d expect to exist anyway if one is already at the stage of mapping the area of the crosswalk).