If you notice above, USGS doesn’t even bother trying to map the water course through wide dry washes. For the sake of OSM’s data model, I think using waterway=* ways to approximate the water course is worthwhile, especially given the ongoing discussion about mapping virtual waterways.
We might not be having this discussion right now if it weren’t for the effort to analyze the connectedness of waterways in OSM. That depends on having waterway=* ways to make the connections.
That was a combination I thought might work well for the area of the wash. Maybe natural=wash or natural=dry_wash could work to define the area?