Funny . . . but that's not the case. Just like you, I am a cat's whisker from the bottom. The only thing I can refuse are appointment stops that have not been scheduled, residential (if I have a 48 or 53), or tight stops you definitely have to use a 42 ft trailer for. We route our own trailer as we break line haul. Supervisors really don't walk around telling us "do this" or "do that." We're all big boys and know what needs to happen.
Sometimes if I am light on stops, I will call a residential customer from the dock and tell them their shipment just came in and I can put it out for delivery today, but they will have to meet me at Walmart; or they can wait until it can be scheduled on a liftgate. Most will gladly take a Walmart-tailgate today over waiting another day or two for curbside delivery. (A driver should never be forced to take a 48 or 53 into a residential neighborhood by any company for any reason)
Senior guys can leave stops for me they don't want, and they do, but they are pretty good about telling me what the problems are with the stop they leave behind. That's the perk of seniority that I'll have someday :)