The noise currents must flow into something. They can't just disappear.
They do not, of course.
For I noise 3 (noise current 3) to exist Vnoise (green) must exist.
For Vnoise to exist we must have Inoise 1 or Inoise 2 or both flowing. We also require a non-zero impedance in the audio cable. Many line cables can run a substantial fraction of an ohm per meter.
Getting very low ground resistance for line cables as remarked, is less easy than (for example) using a 10AWG (6mm^2) Earth connection mains cable is trivial.
According to Kirchoffs law Inoise 1 & Inoise 2 must flow out of the circuit somewhere, they "exit" via the cable to the distribution Panel. From there on they are of no further concern.
Technically speaking neither Inoise 1 or Inoise 2 are of concern either, ONLY Inoise 3 is of concern, because it is the only current that flows where it matters to the audio circuit.
One way for Inoise 3 to exist, we can for example interrupt the current loop for iNoise 1 or Inoise 2 by interrupting (lifting) the Earth, which will then redirect these currents to flow in the audio cable (which is precisely where we do not want it and where it causes noise).
The other is have a non-zero impedance earth connection in the power cords that will cause a the noise Voltage Vnoise to be non-zero and thus redirects a proportion of Inoise 1 & Inoise 2 through the audio cable ground as Inoise 3.
Inoise 3 will however not be affected in any manner whatsoever with any current flowing in the earth conductor exiting our sheet at the bottom or as noted before even a 1kV offset at that point (it's incredibly unsafe though).
Now we have another type of earth loop that indeed may require to break one current path, though it usually preferably to use a different solution.
In this case we actually have two separate circuits with separate spurs to the distribution panel or a ring mains with substantial distance between sockets and often substantial current flow from non audio appliances in either spur or through the ring mains.
This creates a substantial between the two earth pins of the two sockets which are usually at a substantial distance.
In a home environment this may be one or many powered subwoofers placed remote from the main amplifier and plugged into a convenient nearby outlet.
Lifting any of the earth is usually not permitted and the correct solution is to use long power cables on the subwoofers and to plug them into the distribution unit or outlet the Amplifier is plugged into. And again, using "fat mains cables" will produce lower noise than "thin mains cables".
Of course, most real systems tend to have more than two pieces of equipment interconnected and life gets a lot more interesting. As mentioned, SMPS type power solutions add their own challenges.
Having a low ground resistance in signal cables (as low as feasible) is obviously desirable, but I do not see anyone using line cables with 10AWG ground lines and massive connectors with very low resistance any time soon.
Having a separation between Audio Ground and Chassis/Earth is desirable but holds massive EMC challenges (you end up putting EMC capacitors between every connector ground and the case) and electrical safety regulation compliance challenges (the testing currents are VERY high, relatively speaking at 25A RMS), so it is not something seen commonly.
So we are back that easiest point to gain leverage is the mains cable.
QED (again) and now this coon has been well and truely chased up the tree and shot with buck shot from both barrels!
Thor