Bad decision as the cig lighter is connected to your 12V battery which powers the accessories not to the high voltage batteries.
Many EVs automatically charge the 12V battery from the traction battery. Still not ideal, but it does work in a pinch.
Sure, but think of the conversion losses from traction battery -> 12V battery -> mains AC inverter.
In case of an emergency it's definitely usable but not ideal to call it a mainstream use case.
Right, but I was thinking of a full power outlet, which here in Germany can deliver over 3kW. This would enable to run any electric device you can plug in from your car. Very convenient on the road, and as I wrote, a great solution for emergency power.
It seems that the cybertruck will have a power outlet standard, but as the charger electronics already seem to support this, should be an option for all Teslas and other electric vehicles.
You could just connect an inverter directly to the main battery of course but that requires a bit more effort and might cause problems with warranties.