I should clarify our procedure. It's not only done after the second bottle is discharged, but after the fire light extinguishes, whether that is after one or two bottles.
The utility of testing the integrity of the system is obviously to confirm that the light is out because the system is not longer detecting a fire, as opposed to a problem in the fire detection. If everything works as advertised a FAULT light should give an indication of a problem in the detection system, but in the case of a real raging fire, who knows what's going on out there.
Again, after any fire event the crew are going to proceed to the nearest suitable airport and put the thing on the ground, but how the crew handle that divert may be different depending on whether they have a secured engine or a fire that cant be contained.