Firstly, should ATC have even been considering low visibility procedures? I have been banging my head against the wall for years on this matter.
There is difference here between low cloud procedures and low visibility procedures. However, lots of MATS 2, and by default the Aerodrome Manuals do not make a difference.
The pilot operates by visibility only. By all means tell them that the cloud is low and there might be a go-around resulting. However, it means nothing to the flight deck the low cloud thing. The low cloud is meant for the foggy low visibility days as it starts with the cloud ceiling lowering. To get the safeguarding done in time, you can use lowering cloud ceiling as an indicator. There is no indication here of relatively low visibility.
When do you need runway and approach lights? The crew have their various approach light out minima etc. If it was day, then you really need a working PAPI and that is all. It is nice to have the rest working, and they were. It is just that you do not meet the nighttime reversion to standby power.
If you study the nighttime reversion for CAT I, it is a 15 second change over time. This appears to be written on the basis of what diesel generators can do, not what is required for safety. You can survive a loss of lights for about two seconds around flare time, if you have to. Therefore, 15 seconds equals potential prang. Remember Britannia and their 757 excursion?
Was the standby generator the back up power for the ILS? Is there no battery back up for the ILS? Only if there was no battery back up (UPS or whatever), then you would consider making the ILS "uncategorised". However, absolutely nothing has altered the ILS signal characteristics at this point. Nothing has changed the obstacle environment etc.
If you do the risk study, what you have done is to make the system more dangerous. This is not operating in accordance with "as low as reasonably practicable". Therefore, if you are an airport in England and Wales, beware! If you are an airport in Scotland, it is slightly different, but modern interpretation would probably apply from down South. For Norn Iron, no case law...
Overall, I would guess that the airport operator has not done their risk assessments to show that daylight operations with the generator out are acceptable. For night operations, a 15 second change over time does not actually stop the accident anyway
So, at the end of the day, this could all have been solved if you had split low cloud and low visibility procedures. As everywhere else...