When there is a phase to ground fault on the system and maintenance crew are trying to determine the source of the fault, they are even more danger considering first of all they are working on an energized system and the potential to having a phase to phase fault before resolving the first, can be potentially dangerous to life and the electrical system as a whole, also considering the heavy wear and tear of the insulation on the system and the shutdown time and cost if a fatally occurs. Why are modern engineers still designing and recommending the system?
These systems are used where continuity of supply is particularly important, including in hospitals, ships, and some industrial processes. The outage rate is much lower with a properly maintained HRG system.
A second fault on a properly designed HRG system is no more dangerous and no more likely than a first fault on a solidly earthed system. Both are cleared by conventional protection and safety is provided (where relevant) by protective earthing and or leakage protection. There is no "wear" on the insulation, although there is increased stress (compared with a solidly earthed system), and for this reason the insulation (and surge arrestors) are specified with more withstand.
There now exist insulation monitoring methods that allow the faulted part of the network to be distinguished, can be used even on systems with VFDs, and are practicable to be pre-installed at least to feeder level (No requirement to apply clamp-on CTs to live conductors, and it is debatable how dangerous this is since in most cases the CTs can be placed on cables. No need to open live switchboards, and the cables are often in open ladders and accessible to all).
Further sectionalizing to individual load level can be done by switching out loads one by one. Done in a controlled way (as opposed to an unplanned protection trip) by swapping from the running to the backup motor this need not interrupt the process).
With a HRG system the fault is limited through the resistor and while it is true that the voltage level on the two unfaulted phases will rise to line to line levels, the insulation threshold on 480v or 600v cable is sufficient. Secondarily, there is the option with the latest relays to trip the fault feeder or phase in a predetermined manner. HRG systems are not subject to transient over-voltages as ungrounded systems are and have a lower likelihood of arc flash issues. So why are they still being recommended, because they are safer.