power - A question about earth ground and current loop

If the live wire in above illustration touches to the metal case, a high short circuit current will flow to the earth through the safety earth wire and the fuse will trip.

Now imagine a 9V battery staying on a wooden table. If now its plus terminal is tied to the earth through a wire almost no current will flow.

Above two points shows that it is not the case that the earth is a reservoir that sucks all electrons, but simply current needs a loop to flow.

In the battery case it is obvious that there is no loop because the negative terminal is floating.

But what is the loop in the first AC case? Is that the AC generator star connection? Can you draw this loop to illustrate better?

Answer

What is different is that for a battery there is not other connection to ground, this is not the case with the mains.

In the mains, the neutral connection is actually grounded as it enters your building, or at the transformer.

As such shorting the live wire to the case is really shorting the live wire to the neutral side of the transformer through the ground line creating a loop, and, as you have expressed, large current flows till the fuse of breaker trips.

^{simulate this circuit – Schematic created using CircuitLab}

Which is why this is dangerous...

With an isolation transformer you isolate the power from ground and there is no return path.