Another benefit of running either a shutoff delay or battery is that if you're in a fender-bender, you can turn the engine off, put the key in your pocket, go talk with the other motorist and have the conversation captured (at least the video). Without delay, I would be uncomfortable leaving the key in the aux position to continue recording. Who knows how long the conversation will take? I don't know that I would have the presence of mind to even remember to do so. Or perhaps the fender-bender was staged and someone is waiting behind a parked car to jump into my car...
Safety always comes first, and leaving a key in an unattended car is never a good idea...