Two Missouri police officers were indicted separately this week and accused of similar crimes — pulling over women and searching their phones to find nude photos.
Never give cops your phone, yes. Also, don't use biometrics to lock your phone. Police can legally force you to unlock with your thumb print, they legally (and like, physically) cannot force you to reveal a passcode stored only in your brain.
Just to be clear, they can't legally search your phone at all without either consent or a warrant. There is absolutely no reason you need to hand your phone to a cop during a traffic stop, no matter how it is secured.
That dials 911 on Android. That was a fun feature to discover on my new phone. I'm sitting there, trying to turn up the volume for a podcast and it's not working. Pull my phone out of my pocket and see that it's on a countdown before it dials out! The count is down to 3! No, no, no, no, no, no, no! Cancel! Hang up! What the fuck!? Why is that a thing!?
A useful aspect of Lockdown mode (on top of it potentially being quick) is that you can still get into the camera without unlocking it (for me it's a double tap on the power). When you're locked down they can't navigate to your photos, but you might want to be able to record things.