- A neutral wire is one of the two, three or four wires used to deliver electricity. The neutral wire is grounded at the entrance/main panel and therefore its potential is close to zero. Other wires (line wires) are hot or live.
If the neutral wire was not grounded, the electricity would be still delivered to the devices, but the standard earth protection system would not work.
- With some exceptions, the distribution of electricity does not rely on the conductivity of the earth: it is distributed through wires - at least two wires for each destination.
There are systems like SWER (Single-Wire Earth Return) where the electricity is delivered by one wire with the return current flowing through the earth. They are not very efficient and they are mostly used to power some remote loads, in many cases consuming relatively low power.
SWER transmission lines, as all long haul power transmission lines, operate at high voltages (tens of kilovolts) and therefore carry relatively low currents, so the losses due to the earth resistance are not very high. Besides, the connections to the ground are done with long rods reaching ground waters, so it is not just dirt and stones. After the step down transformer, where the current increases, the electricity is carried by two wires.
The conductivity of the earth is roughly the same for DC and low frequency AC currents. In both cases through, you need to go deep under ground to achieve low resistance.
Grounding of the equipment housing keeps its potential at near zero level even when it comes in contact with a live (hot) wire. This system is well described on numerous websites. The illustration below will hopefully make it easier to understand.
Here red is a line wire, blue - neutral and green - ground. For more details, you can check out this post.
Under ideal conditions, connecting the housing to the neutral wire (grounded at the main panel) would work fine as well. But in the real world it is not such a good proposition: besides some more subtle reasons, an accidental break of the neutral wire, leading to a device grounded in such fashion, will bring the housing of the device to the line voltage, which could be lethal. Grounding the housing by a separate ground wire adds redundancy and therefore is more safe.