J.J. wrote:
"---why do we need a ground wire at all?"

Three reasons:
1) 50/60 Hz safety
2) R-F circuitry or suppression
3) Lightning abatement

Powerline frequencies have such wavelength that phase and voltage are
the same everywhere along a line in any particular vicinity. Wire
inductance is of little consequence.

Balanced R-F circuits don`t rely on ground wires to convey signal
between points. Transmission lines do this. Ground wires may be used to
supress some undesired R-F appearances.

Ground wires are essential to lightning abatement as the earth is nearly
always part of the circuit.

Best regards, Richard Harrison, KB5WZI