A typical passenger vehicle might only have a 50 amp hour battery. Even a large pickup truck might only max out with a stock 100 amp hour battery. Definitely dont have "hundreds of amp hours available."
Ive got a system that's supposed to be low powered since it's a Via 2.0ghz based system, but I still measured the power consumption to be 6 amps which is a considerable amount in relation to the total amp-hours available. 12V or 11.5V is a good loaded voltage to cut off the system because once you unload, then the battery voltage is most likely going to jump up a bit. However, by definition, 12V unloaded (steady state) is practically considered to be 100% discharged for a lead acid.