why not simply make the signal pair as follows:
D+ = V_SIGNAL
D- = V_GROUND
I assume you mean that the V_GROUND signal would be connected to the circuit ground at one end or the other of the link. Maybe at both ends.
If you do this, you are no longer doing differential signalling, you are doing plain old single-ended or unbalanced signalling.
So the question you're really asking is, When do we use differential signals and when do we use single-ended signals?
Single-ended signals are used in lots of situations. Most traces on a PCB are typically unbalanced signals. For short connections with slowly-changing signals over a ribbon cable between boards, we often use single-ended signals. Even for long connections between boxes, unbalanced signals can still be used.
But to achieve good noise immunity and low radiated emissions, for reasonably fast signals over "long" distances, unbalanced signals typically require a shielded cable, such as coax.
But coax is more expensive than the now-ubiquitous unshielded twisted pair (UTP) cable.
So we'd rather, if we can get away with it, use UTP.
Now, if we drive a signal on one line of a UTP connection, we can, like you say, eliminate common-mode interference by receiving the signal at the other end with a differential receiver (V_SIGNAL = V+ - V-). But look at the signal we're sending out on the cable. The signal we're generating has a substantial common mode component.
V_CM = 0.5 * (D+ + D-)
Because of this common mode signal, our system is likely to radiate strongly, which will make it difficult to sell in most jurisdictions.
So really, we are using differential signalling to allow us to use low-cost UTP wiring with reasonable (hopefully conforming to standards) radiated emissions. In some cases we might still prefer unbalanced signals on shielded cables when the system requirements (very low emissions or very stringent immunity requirements) justify the cost.
Even over short distances within a box, we might use differential signalling on untwisted cable (such as common ribbon cable) to reduce emissions at a lower cost than using shielded cables.
What is the typical return path for current driven on the differential pair?
The currents on the two conductors of a differential pair (for a differential signal) are equal and opposite. You could say that each one of the conductors is the return path for the other one, or you could say that the net current is zero, so no return path is necessary.
Of course if you launch a common-mode signal on the differential pair, its current will need to return somehow. If there's no designed return path for the common-mode signal, it could travel over a large loop and cause significant EMC issues.
What, exactly, about the differential pair signalling causes the EMR cancellation?
Because the two wires are closely coupled to each other, there is a small loop area between them and so the possibility to generate magnetic fields is small. But you could achieve the same thing with a well-designed single-ended transmission line.
In twisted pair, you have alternating loops where the magnetic field will be in opposite directions. In the far field, the contributions from the alternating loops will tend to cancel each other out, resulting in very little radiation. There will also be a similar effect for susceptabilty.