I think dragging in fortress mode is a little unnecessary, except perhaps in the case of a swimmer rescuing a non-swimmer, or a dwarf on the bank dragging out a drowning dwarf standing near the water's edge. Dragging doors and other objects around that they already carry effortlessly.. I fail to see the benefit. If you don't want to picture them hefting a giant stone door on their shoulder, imagine them dragging it. If Toady required 4 dwarves to drag every stone door from a stockpile to its construction site, everyone would just complain. Some dwarf would cancel because of lizards or because he was thirsty or wanted to take a nap and the others would just wait for him to come back. Not to mention you'd suddenly need an army of haulers for the simplest tasks.
Dragging in adventure mode seems great, though. I shouldn't be able to pick up an entire bin and stuff it in my backback to carry around a few thousand miles before I throw it at a minotaur. Maybe quests could be implemented where you need to drag a person - perhaps a runaway slave, a fugitive from justice, or even a wounded person who needs rescuing from a goblin tower.
In a related note, pack animals could drag plows for faster farming, or wagons for hauling large amounts of heavy materials about. Imagine setting up a quarry on your map outside your fortress, because you want bauxite or obsidian or something not where you started digging, and instead of having that army of haulers carry stones back one by one, they drag it to a nearby wagon and then the beasts pull the wagon back to the fort once it's full.