The person(s) using said device are more than capable of doing it themselves every time they use/move/connect the device. It doesn't take any special skill or expertise to see that something is damaged and shouldn't be used.
That may be true of the colleagues you work with, but having attended multiple electrical fires caused by people (ab)using cabling there are plenty of people out there who wont even follow basic safety instructions.
I'm not doubting your experience, but I've been volunteering in the fire brigade for about 20 years now and even during my time as a General Duties police officer, I don't think I ever once attended a structure fire caused by a faulty appliance cable. Also, the vast majority of "electrical fires" occur at home (people leaving heaters too close to combustable materials, not cleaning the lint trap in their dryer etc...), which wouldn't be applicable to portable appliance testing anyway, since 99.99% of people don't have their appliances tagged and tested at home, it's almost exclusively a process for commercial and industrial premises.
The only time I came close to a house fire was when I visited a friend's house and could smell smoke. Turned out someone had used the improper fuse wire in a very old fuse box and was overloading the power outlet with a double-adapter.
If we're talking about commercial premises, I cited an example earlier where an office nearly burnt down due to a faulty appliance that was not detected/identified during a tag and test just a day before.
Have fires occured previously because of a faulty appliance lead? Sure, but I dare say in very small numbers. Is it worth the effort of PAT? Probably not, especially considering that the test result is only really valid at that specific moment in time. A "pass" means almost nothing hours, days, weeks later. At that stage, we're back to using our eyes and judgement.