A question about remote ground sensing and its advantages
With ground at two remote points there will inevitably be ground currents (from other equipment also) circulating that cause interfering volt drops between sending end and receiving end. This produces an error and degrades your signal. That’s usually regarded as the primary issue.

A secondary issue is that the impedance seen on hot and common wires from the perspective of electric or magnetic field interference is vastly different. This means interference cannot be coped with to any significant degree. In the original circuit, the impedance to ground on both wires is generally equal.