This scheme is very effective in eliminating ground loops. When noise enters a shield connection only to earth, that noise can't enter the signal path. Implementing this approach requires balanced lines and transformers since ground is not carried between components. There is still debate about the use of transformers in modern audio equipment though. The main reason we ground a sound system is for safety.
Proper grounding can prevent lethal shocks.
The next reason for grounding a system that includes AC powered equipment is that proper grounding may reduce external noise pickup. The earth ground, required by electrical codes everywhere, can contribute to ground loops. With just one path to ground, there can't be a ground loop. A ground connection through the AC cables and the chassis of the two units campletes the second ground connection. One way to break this ground loop is to lift the AC ground on one piece of equipment, typically the power amplifier.