Why do we need to starve the engine before turning it off?
The reason is the large spinning thing on the front. Residual fuel in the engine has been known to auto-ignite (i.e. combust without a spark), causing the prop to spin, causing serious injuries and deaths. A lean cutoff reduces the risk that someone handling the prop will get maimed or killed. 

In a car when you turn the engine off usually it is in park or neutral, so if the engine turns a few revs the car goes nowhere, even if it is in gear the car may lurch but that's generally it. Modern car engines have electronic fuel injection and electric fuel pumps, some modern push-button gasoline engines are stopped by performing a lean cut-off, turning off the injectors before the plugs, most work by just stopping ignition. Diesels don't have spark plugs, they rely on compression alone, so cutting off fuel is the only way to stop them.