To understand the reason for the GF protection of conductors on services or feeders of 1K amps or above is to understand the reason behind it.
There is a limit to the amount of current that grounding pathways can handle before catastrophic failure occurs, these requirements are also limited to a voltage of 150 volts up to 600 volts, I have never understood why it wasn't continued above 600 volts because the available energy is even more? of course it's not common to have circuits at or above 1KA above 600 volts but they are still out there.
The amount of energy in a catastrophic failure of a grounding pathway at these voltages and current can very bad not only in the causing a fire sense, but in the event that a person or persons are within the area of the failure point, which now we are including Arc flash events, also the failure of the grounding pathways can also allow the grounding system to rise above earth potential so now we also have a shock hazard from anything grounded to this grounding system past the point of the grounding system failure.
Now you mentioned that the X0 is bonded on the transformer but no neutral is used, I must ask this, do you have a system bonding jumper run to the first disconnect from the X0 to the system grounding point at the first disconnect? (I would believe that this is the 4,000 amp disconnect), and all EGC's and GEC's are bonded at this point or to the transformer's X0, if you do not have this then you have a very potentially dangerous system as you do not have a fault clearing path and any first fault to ground can cause the system grounding to rise to the 277 volts of the phase to X0 voltage and Earth, this means a person who comes into contact with anything part of the grounding system and Earth after a first fault will receive a 277 volt potential voltage across their body, The reason the NEC started requiring the neutral to be extended to the first disconnect was to eliminate this very problem, to give the grounding system a reference to the X0 of the transformer anytime the X0 is bonded.
Not only was the lack of installing a neutral and you mentioning that the X0 was bonded, but the fact you mentioned about the alarm requirement of an ungrounded system, this is why I asked the above question, if you intend to have an ungrounded system then you need to remove the X0 bond and install the GF alarm system.
When we have the X0 bonded which will also be bonded to the primary grounded neutral which will have reference to Earth, and we don't run a low impedance path to the grounding system of the building then we set up the potential that after a first fault which only sounds or flashes an alarm until a more convenient time can be made to shut the system down and repair the fault, there will be a high potential (phase to X0 voltage) between the buildings grounding system and Earth, any electrode system will not have a low enough impedance to make this safe or cause any breaker to open, this is why if we intend to install an ungrounded system we must not have the X0 of the transformer feeding the buildings electrical system to have any reference to Earth, because once you have reference Earth you must have a low impedance path between the X0 and the buildings grounding system and Earth can not be used as this pathway.
I have seen the above happen when an unknowing line man changed out a ungrounded 480 volt delta transformer and only had a set of 277 WYE tanks to use, and made the mistake of bonding the X0 at the pole tanks across the street, we got lucky and caught it before a first fault happened, the service was as designed an ungrounded system so there was no grounded conductor ran which left only the Earth as a pathway for the first fault current to flow back to the X0, if a first fault was to happen the whole building including the metal siding would have been at a 277 volt potential to Earth.
Don't get me wrong I have no problems with ungrounded systems, and from an arc flash point of view in some ways they can be a little safer because you have one less pathway to create an arc flash, and for something like a data center or web hosting center, it would be a great reason to have the extra protection of not going down until a second fault occurs, to me an ungrounded system would be the correct choice for a building like this, and the fact that if any grounded systems are needed they can be created in house through any SDS transformers without affecting the main ungrounded system and its two faults before failure protection.
Also exception 2 to 215.10 does not require another GFP on a feeder if GFP has been installed ahead of this feeder as long as there are no transformers between them, a ground fault on the secondaries of a transformer will only produce a line to line current to the primaries of a transformer so a GFP device ahead of a transformer will not detect a ground fault on the secondary of a transformer so in this case another GFP will be required if the feeder meets the requirement for GFP.
But you might not want to have the main GFP tripping out on a GF on a feeder or branch circuit so using GFP's on feeders can be a way to provide system coordination to prevent this.
Another point is even with ungrounded systems GFP's are still required because the grounding system can still be subject to the high current if a second fault event happened before the first fault is repaired, or if two or more phases go to ground at the same time.
One little point about GFP's, they always come shipped from the manufacture set to their lowest settings, as electricians we are not considered qualified to make the calculations for these settings, and the liability of doing so is to high to even think about doing this, so expect to have an engineer to do this part of the setting of the GFP systems, this engineer should also be the one who does the coordination study so you don't have branch circuits taking out feeder breakers or the GFP's, or feeder circuits taking out the mains.
Hope this helps the understanding part, and sorry for being so long winded but it was allot to cover.