A simple matter of economics, really, and Kirchoffs laws and just simplicity.
If you have a current loop say 5 kilometers long,
and you inject a current of say 10 milliamperes into that loop from a source,
then if you break into that loop at any point and measure the current
it must be 10 milliamperes.
With voltage measurement, over the same distance,
the cable resistance comes into play, however tiny it may be,
which would depend on the device reading the voltage signal.
It would be required to use a second pair of wires to measure the voltage at the source,
an example of this practice being a loadcell.
These sensing wires would also have a resistance, therefore a tiny voltage drop.
A current source on the other hand will automatically compensate for cable resistance.