The water analogy can be used as a rudimentary tool to describe an electronic circuit, but in the case of voltage on a wire, it is exactly analogous. When a voltage on a wire is induced, the power supply or battery is shoving excess charge (which moves to the surface of the conductor) into the copper. Yes there is an electric field running through the wire, but that field is a product of the extra charge on the surface of the conductor. The more charge you shove onto the surface of the wire, the higher the voltage (with a constant reference). So why isn't voltage explained exactly like this to beginners? Instead of starting with the electric field running through the wire, why not just explain it as electron pressure? Is this just a subjective case where it's more intuitive to only myself?