If you were to place many ground rods in succession and maybe create some sort of bonding of the entire earth from the rod at the house all the way to the rod at the transformer, then you couldn’t get a difference in potential between a hot conductor shorted to the ground rod and ground surrounding it, right? Would that be comparable to equipotential bonding by eliminating touch potential of the ground rod?
Any time current is flowing through a regular (not super-) conductor, the conductor has resistance, and the resistance of the conductor means there will be a voltage difference between the two ends of the conductor. Via V = I * R (Ohm's Law), where R is the resistance of the conductor. So if the conductor is 100' and has a resistance 0.2 ohms (i.e. #12 copper), that would make the voltage difference 2 volts (10 amps * 0.2 ohms).
In your example, you've actually created a circuit that doesn't require any path through earth. The ground rod at the transformer will be bonded to the secondary neutral, I believe, and since you've bonded all the ground rods together, and you shorted the ungrounded (hot) conductor to one of those ground rods, there's a wire path to create a circuit. You've just referenced that wire to earth in many places. [And so to the extent that the path from ground rod to ground through earth is viable, it will carry some current in parallel with the wire path, in proportion to its resistance vs the wire's resistance. If that resistance is say 200 ohms, then it will carry 1/1000 of the current, or 10 milliamps when the bonding conductor is carrying 10 amps.]
A more interesting example is to not have the bonding conductor present, so the earth path is the only path. With 200 ohms for the earth path, and if we ignore the resistance of the wires, and we impose 120V from the house ground rod to the transformer ground rod, we should get a current of 0.6A amps. If we hook a voltmeter up between the two ground rods, we'll get a measurement of 120V. [If those other wires we ignore had a resistance of 1 ohm, then we'd really get (200/201) * 120V, which is basically 120V, which is why I'm ignoring the wires here.]
But what if we check the voltage between the ground rod 1/4 of the way between the house and the transformer? If the resistance from the ground path is primarily due to the earth itself, and not the resistance of the interface between the earth and the rod, we'd get a measurement of 30V (or 90V, depending on which end rod you measure against). While if the resistance is primarily between each rod and "bulk earth", with bulk earth having very low resistance (once you get away from the rod, there are many, many different paths available for current through the volume of earth separating the rods), then you'd expect to get around 60V (assuming each rod has about the same resistance to bulk earth).
I am fairly sure, but not certain, that the latter is typical.
Cheers, Wayne