One important reason for HRG systems vs. ungrounded systems is to significantly reduce the transient over voltages that can occur with re-striking ground-fault arcing. Such over voltage can result from successive charging of line-to-ground capacitance, and also resonances of the capacitance with the line inductance (more significant with longer lines). The grounding resistor acts to dampen these events by absorbing energy that might otherwise be accumulated in the reactive elements (capacitance or inductance).
When a grounding transformer like a zig-zag or wye-delta is used with a grounding resistor, a minimal current should normally flow through this resistor, because of the currents through the line-ground capacitances will be substantially equal in magnitude and 120° from each other. That would not be the case if a resistor was used for corner grounding, because the capacitance to ground on the resistively grounded line would have a minimal voltage across it, and therefore minimal current flowing through it. The resulting current imbalance would cause a higher nominal current through a grounding resistor than with a grounding transformer approach. As Jon mentioned above, this could make accurate ground fault detection more problematic. Also, a given resistance would have to continuously dissipate more power due to the unbalanced capacitive currents, even in the absence of any ground fault.