I wonder if visibility was good enough that looking both ways before crossing the runway would have prevented this.
No. it wasn't. Delta crosses 04 in diagonal, so basically they should have taken the head out of the window and look behind. They had the clearance, so they just tried to cross. The problem is for some reason they did not hear the "Truck 1 stop" call.
That'll be one of the things the NTSB investigates.
I also wonder if you're down to a "one controller" scenario if it would be better for there to be once frequency, not a ground/air split.