> in fact this is appropriate after all, with cyclelists having right of way over cars at this junction without dismounting?

Yeah that's my interpretation based on https://www.vdot.virginia.gov/travel-traffic/bike-ped/bike-safety/ and the related legislation, as the trail here doesn't have signage but the crossing is clearly marked. Not only do cyclists not have to dismount, they don't have to stop or yield (unless the car is already "in the intersection", so to speak).

I think the explicit crossing is helpful from several perspectives. It expresses the legislative intent of the segment, as well as the details of path use (surface, markings, etc). Routing apps might use that information to provide a faster route, or to caution of an upcoming yield-crossing.