Just out of curiosity, I'm wondering why car chargers can provide no power when the car is off in most cars. Is it because the electrical system that connects to the car chargers is running off the alternator and not the battery?
in most cars the cigarette lighter socket is on the accessory circuit and is only active when the key is in the accessory or run positions.
some cars have it always live.
I would suspect that it's done to stop you leaving something charging while you go shopping then coming back to find you don't have enough battery power to start the car. A former car of mine had the cigarette lighter fused at 10A, which can drain a 35AH battery surprisingly quickly.