Thanks, everyone, for sharing your perspectives 
Let’s take a look at this very common situation:
If you believe this is not a footway=crossing - how would you like to see it tagged?
(“I wouldn’t map this!” is not the point; assume others are mapping them - because we are - and the goal is to limit the dilution of the footway=crossing and highway=crossing tags by mappers like me by having a different tag for “not-crossings” that aren’t in the primary roadbed.)
As for why I care to map them: These are locations where my risk as a pedestrian of being hit by a car is quite significant. I want routers to be able to route me along the north side of the street that has 40 ft of “not-crossings” vs the southern side of the street with 200 ft of them.
I want those with vision and mobility impairments to be able to know when they’re moving from a relatively safe sidewalk into the path of reckless vehicles, whether there are incline changes or tactile paving surfaces on either side, and the length of the “not-crossing”.
Yes, I guess it’s technically possible by looking for width=* tags on any intersecting highway=service, but in my experience that is very infrequently tagged.
Random aside: “not-crossings” keeps reminding me of “not-turtles” from The Mercy of Gods, which I really enjoyed.
Thread continues here: Intersections of Sidewalks and Driveways - #35 by Lumikeiju