On the other hand, when I'm pulled over, I definitely want my phone to be recording audio.

Agreed. Opening the settings and disabling the fingerprint scanner would be easier and allow you to still use the device to record audio.

And then you get shot because the cop saw you "reaching for a gun" instead of putting your hands in view on the wheel as soon as you're stopped.

would be better to have an app that does it so you don't need to fumble through settings

Or consider using a dash cam with audio recording.