The PSU serves the shield everything from the outside world, the vast majority of them are plugged straight into a wall outlet not a UPS so there is zero expectation that power will be shut off before they are plugged in or removed.
Godto, that is a dumb example, it is the equivalent of saying you always make sure you take the oil out of your car when performing deep engine work, wouldn't you do the same to change the headlight? No, i wouldn't because i understand what is going on and that fully assembled systems are much more protected and stable than their individual components are. Once you have everything in the case with the PSU in it you will actually have a very difficult time damaging the internals with any external source, PSUs can only hurt the internals when their secondary side blows out, any damage from the line would only hurt the primary side which is isolated.
You will do zero harm to the components of the system by plugging and unplugging the PSU while the UPS is on.