In my 4 years as a DL PM, I have heard DL ask for volunteers once or twice. I wish they asked more, as most of the time I would certainly give up my seat for compensation.
I remember when I used to fly UA MCO-LAX-MCO weekly. They asked for volunteers every Thursday on the LAX-MCO red eye. Back then, I had no interest in travel other than for business so I never gave up my seat.