I think you have it the wrong way around. Geomagnetically induced currents (GICs) are more prevalent in high-voltage wires because they have low DC resistance. The longer a line, the larger the induced voltage. High-voltage lines can extend up to 1,000s of km, as they are most efficient. Then its basically V=IR. So low-resistance wires and long distances = larger GICs.

The danger is not from the cables burning out (extreme GIC events can lead to a couple of hundred Amps, which shouldn't be a problem for the cables), but the addition of the DC current in an operational transformer will push it into core saturation leading to nasty effects. Twisted/untwisted cables don't come into it.

Source: postdoc who models Carrington-scale events, and did my PhD on GICs in a regional power network.