It was 1996 and I was a student at BYU, and it was the worst calling I have ever had in the church. It was an established Provo family ward (not a student ward) that had lots of apartments and cheap crappy housing, mixed with an established neighborhood of ward old-timers. After only two months, the newly-called EQP had had enough of moving people, so he went to the Bishop and got permission to create the calling of "Moving Committee Chairman." I was the lucky guy. The job description was basically to move people who hadn't packed anything almost every weekend. And since I was "Chairman" of a "Committee" it meant I was the guy responsible for harassing the Elders of the ward for help on a weekly basis. I don't recall there being any other members of the so-called "committee." For several moves it was just me and maybe one other guy.
My experience with moving people in and out in other established, non-transient wards, in another state, has been far better. I don't mind unloading and loading trucks, if people have made some kind of effort (which most people have done) and I agree it's a great opportunity for service and fellowship.