Breakdown voltage is pressure dependent, not a constant.
Your figure is for (eyeballing a graph) approximately 2e-2 torr and 150 torr, less between, rapidly increasing with harder vacuum. The extreme limit even in a perfect vacuum is ~1.32e18 volts per meter due to pair production.
For a sense of "perfect" vacuum: if I used Wolfram Alpha right just now, the mean free path of particles at the Kármán line is about 15 cm, becomes hundreds of meters at 200km.
Though this assumes a free floating measurement, the practical results from https://en.wikipedia.org/wiki/Wake_Shield_Facility would also matter here.
> And you're operating this in space where you have ionizing radiation. Free electrons with a big voltage differential?
Mm.
Possibly. But see previous about mean free paths, not much actual stuff up there. From an (admittedly quick) perusal of the literature, the particle density of the Van Allen belts is order-of 1e4-1e5 per cubic meter, so the entire mass of the structure is only order-of a kilogram: https://www.wolframalpha.com/input?i=%284%2F3%29π%282%5E3-1%...
If this is an important constraint, this would actually be a good use for a some-mega-amps current, regardless of voltage drop between supply and return paths due to load. Or, same effect, coil the wires. And they'd already necessarily be coiled to do anything useful: Use the current itself to magnetically shield everything from the Van Allen belts.
Superconductors would only need a few square centimetres cross section to carry mega-amps, given their critical current limit at liquid nitrogen temperatures can be kilo-amps per mm^2.
But once you're talking about a 36,000 km long superconducting wire with a mega-amp current, you could also do a whole bunch of other fun stuff; lying them in concentric circular rings in the Sahara would give you a very silly, but effective, magnetic catapult. (This will upset a lot of people, and likely a lot of animals, so don't do that on Earth).
