And even if the earth/ground potential at the power plant and where you are is the same, current flowing through the neutral means that your end of the neutral wire might be dangerously above or below earth/ground potential which is also a shock hazard.
Not sure where in the world you are, but here in Australia (and many other parts of the world) we have what is known as the "MEN" system - Multiple Earth/Neutral.
Each connection point to the grid (house, office, remote pump, whatever) is required to have its own local earth. This is usually an appropriate sized ground stake and/or good bond to the water pipes.
The grid "Neutral" and the local "Earth" are bonded at a single point in the switchboard. That's the ONLY place the earth and neutral are bonded for that site. (This is important later).
The grid "Neutral" actually carries virtually no current at all, and certainly does NOT connect all the way back to the power station (not here anyway). Power is distributed as 3-phase, where the 3 phases are electrically 120 degrees to each other. Given enough loads (thousands of houses), connected from one phase to the "star" point ("Neutral", the loads all balance each other and the only current in the neutral is any fault or "out of balance" current. Usually very small.
Back at the house, by tying (bonding) the earth and neutral, you prevent your local neutral from having a major potential difference to all your "grounded" household parts (exposed metal in your sink or bath, for example). The single earth bond also lets you use "RCD" (Residal Current Detectors, or "core balance" or "Earth Leakage Circuit Breakers" - all basically the same thing) actually monitor your power circuit for faults. If power flows through the active, but NOT back through the neutral, the difference is flowing somewhere via "ground" - like someone throws the toaster in the bath with you - and very quickly disconnects the power, hopefully saving your life.