At 6cm spacing, a 10km by 10km ground array with 1mm^2 cross section wires has total 1667 m^3 volume; this is as much conductor as you would get in the equivalent of a 1111 km long 1 GW HVDC cable:
https://www.wolframalpha.com/input?i=10km*10km%2F6cm*1mm%5E2...It's not exactly the same thing, of course, but it means 40 such ground stations would use as much metal as a 1 GW line looping all the way around the planet and back to itself, and a global grid is another way to obviate storage.
That's 1 GW with standard existing cables; I assume if you actually want to go that far one can improve the design as the optimisation goals are different. Parallel cables lower resistance.
I'm also not sure how much maximum current would scale in such cases.