Ok skipping ahead.
120 volt delta is extremely rare in the US, plus I have never seen it provided from a poco. But, it is well more then possible to pull off. I have done it before with control transformers. Anyway, Nearly all utility transformers are 120/240. Each unit has 2 120 volt windings. These may either be connected in series of parallel. For 120/240 services they are connected in series and the center bushing is grounded. For 120/208 services the windings are connected in parallel and only 2 of the bushings are used on the transformer itself. Each pole now unit gives 120 volts only. A jumper is made from the X2 bushing on each unit to the next. This is the neutral and its finally drawn away from the bank after hitting all 3 and grounded. From each X1 comes 1 phase conductor. This is normally how a 120/208 service is done using 3 single phase banks. In the old days when 240 and 480 delta were the norm for every other service pocos would do the same, keeping 240/480 rated units on hand which could serve both needs just be reconnecting the windings in series for 480 and parallel for 240. Polarity is followed as with any delta. This allows only 1 type of transformer to be in stock yet both needs can be met. In your case the transformers would be rated 120/240, windings connected in parallel for 120 volts and the 2 bushing would be connected in delta rather then wye. 120 delta rather than 120/208Y.
How old is the bank btw? If its from before the 40s such a thing could be done without raising a red flag since no solid standards existed yet in the NEC. Heck fusing the neutrals was also the norm up until this point. In addition back then in the early days of electrification pocos were willing to give you any service requested. Most probable scenario Power being new to the area some industrial electrician seeing only 120 volt loads thought it would be easier to just ask poco for a delta over a wye because it would be simpler to bring 3 wires instead of 4. Either that service continuity may have been a requirement if manufacturing was involved.
I am surprised National grid hasn't asked this to be changed out yet. Even the common 120/240 high legs are being forced out of service working or not. Keeping it by itself shouldn't be an issue, however one possible problem I can see is if the bank ever needed to be replaced. A careless lineman not knowing what he is doing might end up putting in a 240 volt delta bank instead of a 120 which would be a disaster. Chances go up if its during an after storm emergency restoration. And a good fire if nobody is there to catch it in time.
As for the system itself as long as it is grounded and bonded like any other system (has equipment grounds, panel ground bar, gec, water bond ect) and a working ground fault detector it should be safe. 2 pole breakers must also be used but they wont be effected by the lower voltage. 95% of Norway's residential and commercial power systems are operated ungrounded, running at 230 instead of our 120, so don't worry about this concept being unproven. 98% of the appliances being used wont care since the are only looking for 120 between the prongs.
The down side however is it will not be code complaint. The only place the NEC recognizes ungrounded 120 volt power is in hospitals for critical care patient equipment found in intensive care units and operating rooms. These are fed from a dedicated panel with an isolation transformer, ground detector, ect ect. The 2 main goals being to reduce the shock level should someone come in contact between a phase and ground in addition to being able to still have power should one phase become grounded somewhere.
In your case incandescent screw shell sockets would not be compliant, and depending on whos relamping that might be an issue should one touch the screw shell while in contact with the bulb. Double pole switches would make it safe for hard wired fixtures but not for table lamps. The other issue that might come up is with an appliance needing a ground reference. Some furnaces with electronic ignition require a ground reference for the flame sensor circuit. With the ungrounded source the furnace may shut down on error codes. The final issue would be if someone did not know what they were working with, which as you can imagine would be frequent. But outside of that everything would function as normal.
Hope this help.
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