I would like to know what those problems are and why grounded systems seem to be preferred. I really have never heard any concise explanation. Maybe there is a utility EE on here that can give some specific documented reasons and examples.
GoldDigger said some of the same but here ya go:
Ungrounded systems are weakly coupled to ground through a capacitive reactance. Grounding helps mitigate the problem of high L-G voltages that cause insulation failures and personnel hazards. The effective LC circuit resonance can cause L-G voltages of at least twice normal. Re-striking arc faults can generate L-G voltages of up to six times normal.
So, in general, grounding the utility distribution:
Assists in proper device operation
Increases safety during normal and fault conditions
Helps stabilize voltage during transient conditions
Helps dissipate lightning
Examples of benefits:
Improved Surge protection
Higher relay current (lowers fault path impedance)
May allow a lower equipment BIL rating
May allow one conductor to serve as both primary and secondary neutral conductor.
May allow lower equipment costs (fewer bushings, fewer cutouts, reduced insulation, etc)
May reduce losses when earth is used as a parallel conductor.
Helps maintain neutral stability
Easier to detect ground faults