Why do I ground my transformers? For single phase (120/240V) NFPA 70 / NEC requires it.
So why does NFPA require it? According to Article 250.4(A)(1), the purpose of electrical system grounding is, “To limit the voltage imposed by lightning, line surges, or unintentional contact with higher-voltage lines that will stabilize the voltage to earth during normal operation.”
However, documents from the time when they switched from having transformers not grounded to grounded, indicate that the switch was to prevent fires. If a transformer got a short from the primary side to the secondary side of the transformer, the secondary would have a very high voltage to ground, as the primary supply is a grounded supply. The high voltage would break down insulation, let current flow, overheat wiring and cause fires. Likewise, equipment that was grounded would also allow excessive current flow through them, damaging the equipment and causing fires.
This apparently was common enough problem that insurance companies wanted the change. The insulation in transformers wasn't the quality we have today, and they would short internally, or tree branches could fall across the wires going to/from transformers, and etc.
By having the transformers grounded, there is good path to ground, then a the fault would has a high current flow to ground, and fuses will blow reducing the likelihood of a fire.
The trade off, is we have less fires, but get a larger risk of shocks. Back in the early 1900 it was determined that this was the lesser problem. Now that we have things like GFCI's and better fusing/breakers, the risk of electrical shock is even lower.