10MW (about 14000 hp) can be moved with just 100 amps at 100kv. Most houses have something like 100 amp service from the power company. At 1000kv that's only 10 amps. 10MW for 10 min is about 1500kwh or enough to charge some 15 teslas approx to full.
The power levels you're talking about are big compared to household stuff, but kind of a joke compared to industrial processes.
There's no such thing as a consumer grade 11KV insulated cable.
https://www.schleich.com/en/product/high-voltage-cables-en/
I mean you would need some smarts to ensure the leads are never exposed when active but otherwise I don't see the issue.
Don't those voltages leak like crazy across things which a normal person would consider as a safe insulator?
E.g. might some regular dirt on a plastic charging cable leak it into your hands?
Liquid nitrogen can be made from the air on-site if needed, and is a hell of a lot easier to handle then hundreds or thousands of volts.