Wires introduce resistance into a circuit, corresponding to the length of the wire. Because current remains constant in a circuit, voltage must be the variable that changes to account for any differences in wire length. This becomes especially relevant if the signal must travel long distances, as voltage signals will drop along the entire length of the wire. The only way to prevent the voltage drop would be to use a wire that is a perfect conductor without any resistance, which is currently impossible. On the other hand, a signal relying on current (e.g. 4-20 mA) only needs a wire that prevents current from being lost to the environment, which is easily obtainable in practice.
In addition, current is more immune to noise caused by inductive coupling. Inductive coupling is seen when a nearby cable or machine has a changing current. The changing current creates a magnetic field around the cable/machine and this magnetic field interacts with nearby conductors, inducing a voltage. Wastewater treatment and manufacturing facilities often have long runs of cables together where inductive coupling can be an issue, even with shielded cables. Any voltage signal can be disrupted significantly by this type of noise while a current signal would be relatively unaffected.