I always do a run test where possible as, in addition to maybe showing an abnormal current draw, it may expose a problem with excess earth leakage current. You don't say what sort of PSUs. Leakage problems are pretty rare but I have had problems with old, imported, high current PSUs coming over the 3.5mA max. Some rack mount PSUs and UPSs also come in high as they are designed for use in earthed racks not free standing. I've had a couple of PC PSUs (out of 1,000s) go high leakage when they fail but they could still be regarded as potentially dangerous if the PC is left plugged-in despite not working.
The pseudo-leakage tests on some of the newer testers don't seem to be accurate and sometimes don't register at all despite a differential run test showing leakage.
I work in an institution with it's own rules but if I paid someone to PAT a load of PSUs and they omitted all the run tests without consulting me then yes I'd ask them to come back and do it again. (An exception being genuine class 2 IT PSUs in an office environment.)