Way back when I hired out, the first thing I was taught was to let the locomotive do the work. That is, among other things, if the engine is going your way, ride the engine instead of walking or running. The second thing was to make as few moves as possible. Every time the locomotive stops and starts it's another move, and some consider making a hitch a move of its own too. It's not just a matter of economy and savings for the company, it's an economy toward your long-term self preservation. Both mean you'll get less tired and have less chance of getting injured if you economize.
Dropping the caboose (not counted as a separate move since the caboose never stopped its inbound move) instead of stopping and cutting it off and then tying on again later saves 2 moves, especially if the caboose is stopped a little too close to the switch to clear the shove off of the siding. If the caboose is stopped too far back from the switch the shove has to go further away from the switch to get it and the head end brakeman has to walk the additional distance to the engine, if he doesn't want to stand and wait for the train to depart after the air test. And he's needed for the air test anyway since there's no ground air at Carbon Jct so additional walking would require more time.
The other thing at Carbon Jct is the physical characteristics. The west switch is in the beginning of a right curve with the bank/highway on the north side and both the rear of the cars picked up and a 27-car distant caboose would be out of sight of the engine almost as soon as you start shoving out, lasting until you were almost ready to bash the caboose. Even the best crews would probably not want to take that chance (and spill the coffee in the caboose). Since I have yet to see a NG crewman carrying a lunchbox radio in the 60s photos, I assume all moves were still done with hand signals. Dropping the caboose is a more precise operation that saves time, saves 2-3 moves and saves crew ground movements, plain and simple. Work Smart, Work Safe they used to say.