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“Why then, would someone install such an offset system?”
Such an offset system might be considered / installed due to physical and/or HOA constraints at the installation site. In the case I modeled, this was the reality being considered by the poster to which I responded.
“Also, I would expect the radiated signal to be directional on the radial side.”
Others there did also, at first. But buried horizontal wires by themselves when used as an r-f ground produce no useful v-pol, far-field radiation — no matter their physical geometry, or where they are located. All of the useful groundwave radiation from such antenna systems is produced by the vertical conductor extending above the physical earth.
So such buried conductors cannot produce useful directional characteristics to the groundwave fields radiated by a vertical monopole, no matter where those buried conductors are located with respect to the base of that monopole.