To put some of the points into a real-life case, I once chose a fully-flexible ticket for a trip on which I needed it. It wasn't a work trip (I don't need to travel for work) but to go to a funeral which was taking place on a Saturday. Because of work commitments I didn't know whether or when I would be able to fly out, although if I flew I would then have flown back on the Sunday night.

I booked the ticket on the previous Sunday, by which time there wasn't a vast price difference between the fully flexible ticket and the cheapest ticket anyway. The first reservation was to fly out on Monday night and fly back on Sunday night. By 5 pm on Monday I knew that I couldn't go that night, so I called BA and changed the reservation to Tuesday night. The same happened on Tuesday and Wednesday. By 5 pm on Thursday I knew that I couldn't go that night either, and as there was no point in flying on Friday night (I would have missed the funeral by the time I'd got to Durban) the Thursday phone call was simply to cancel the ticket for a full refund.

People who are flying for work will have similar scenarios more often. But even for a non-work passenger, these tickets can have their uses.