Actually your car may use more gas at neutral than engine braking, because at some point on the E46 BMW programmed their DMEs to turn off the injectors when engine braking.
Obviously in this case your engine idling in neutral uses more gas than your engine being turned by the rear wheels but not using any gas.
Also the more your engine brakes, the less you wear on your brakes.
Also, at least in the USA, you don't need to press the shift button to go from Drive to Neutral, but you do to go from Neutral to Reverse. Sadly, that mechanism is there to prevent this sort of incident. While on the topic, you don't have to press the shift button to go from Reverse to Neutral or Neutral to Drive.