Amir says the safety ground does absolutely nothing unless there is a fault in which the case becomes electrified and the safety ground would kick in.
That is correct, kind of. The reason a safety ground is required, and can’t be smaller than the power conductors is the need to carry 100% of a shorting current. That is, if your equipment has a 10A fuse or breaker, the safety ground must be able to carry that current amount safely, but if all is well that current should not flow. However, the construction of a metal chassis which is grounded is rather like a Faraday cage so we expect that RF noise should be greatly reduced vs. a plastic enclosure.
The use of cheater plugs to lift the safety ground becomes a problem when a short happens. The 10A of current, or higher now has to travel 24gauge ground wires in the signal cables, potentially causing a fire or minor explosion or both. If a wire melts fast enough it basically evaporates with a bang.
The problem is how equipment makers connect a signal ground to it, and the center tap of a transformer secondary. In an ideal case there would be no metal to metal path between a signal ground and the chassis, or when used, would not carry from component to component.
Even digital devices can have ground loops as a result of non-isolated coaxial or USB inputs.
The best cases are the use of XLR connectors which allow the lifting of ground on one end or the other, eliminating the loop itself.
