Ungrounded-delta {or even ungrounded-wye} plant distribution has a successful history for process-interruption minimization, but if you don’t act quickly after first fault, it gets messy—potentially with two or more overcurrent devices operating simultaneously. If you want to research this further, there is a {rare} online paper about it —
www.neiengineering.com/papers/paper1JN.pdf for applying such a system one has to be well aware of the first-fault limitation and the need for action when it occurs. It is very problematic if one transformer set feeds two different areas of a plant, or worse yet, two different facilities under different ownership. The tradeoffs have to be carefully understood by all when adopting this system-grounding method.
There is understandable reluctance for many utilities to provide this type of service for their customers because its limitations have to be well understood by all to be effective. It is more likely found in cases where a facility buys power from the utility at medium voltage, or “primary” service, and the plant has complete control over all distribution and loads connected to the {typically 480V or 600V ungrounded-∆} system. If the utility owns the [480-600 or up to 4160V] secondary windings—essentially the grounding “source”, then it may be a poor choice from a reliability and service-continuity standpoint. There will be regional practices and local customs, but in many cases utilities flat out refuse to serve anything except for [480Y/277V or 600Y/347V] 4-wire grounded-wye service to limit repeated ‘rat-race’ complaints and finger-pointing from their customers.
If in the case where [phase-to-neutral loads are served, like 277- or 347-volt lighting loads] the distribution system must be solidly grounded. An absolutely insane stopgap mutation in system grounding is a corner-grounded-delta arrangement, except possibly for an isolated single-transformer/single-motor configuration, for all too often that seems to cause its own set of headaches.