The hospital robots seem like the closest analogue for now, as it's automation being held back by needing to coexist with inferior-performing humans. If it were only robots in the hallway, it'd likely go a lot faster, no? Just like if it were only computers driving the cars, following distances could be greatly reduced because they can react faster.
If it were only robots in the hallways, it wouldn't be a hospital. They did try giving the machines their own pathways. That's what pneumatic tubes were: a fast lane for robotic delivery. Frankly, for a hospital, pneumatic tubes would seem the far more elegant solution.
I guess it boils down to perspective. The hospital robot is in no hurry. His life is no better or worse if he is faster or slower. But a human inside a robot-driven car does care. He doesn't see the overall traffic efficiencies, and even if he did he wouldn't take much notice. All he cares about is getting to the destination asap. So it is a different speed decision than the robot.
The hospital I'm employed at utilizes both pneumatic tubes and robots. Robots roam the basement and employee only areas shuttling around food carts, linen carts, and trash. The pneumatic tube system reaches everywhere in the hospital and sends drugs, lab specimens, and basically anything else small enough to fit in the container.
I knew of a hospital when I was a kid that had raceways mounted just below the ceilings. It was like little toy trains bringing paperwork and drugs to each room. But if you watched them long enough, four-legged critters also used the raceways.
