The weird thing about this claim is that these aren’t deal breakers. It’s possible to get insurance for exotics like McLaren or Bugatti (although no idea if GEICO does those); it just costs a lot.
I’d really like to hear more about those underwriting standards.
There’s a certain point where they become abandoned property, and you can just do with them whatever you want. My guess is that it’s some point after the existing contract runs out, plus 30/90/365 days or whatever. Possibly requiring a court order, public notice, or something else. This will depend entirely on your jurisdiction’s laws on abandoned property.