In defence of my old firm.............
I very much doubt that the engineer needs a bit of paper handed out at the beginning of the day, they didn't fifteen years ago, any way. I don't remember faultsmen ever being given fault reports on paper.
Just because one lives near an exchange doesn't help with speed of repair.
Just because lots of vans are coming and going doesn't mean they are trained or equipped to repair faults.
If you report your fault on line you can see the progress, (or not!) of the fault, at least you would know it's in the system