Both of these methods have an undesirable side effect for me, which is that it immediately pops up the passcode dialog saying that a passcode is required to activate Face ID. Depending on the situation, that could be construed as an attempt to actively interfere with a police investigation, which could bring consequences of its own. It would be better if it silently dropped you to the normal lock screen, and only showed the passcode dialog when you attempt to unlock the phone normally.

Another thing I've often wished for with kids is a mode that removes all notifications and widgets from the lock screen - the only things you should be able to do is to unlock the phone and emergency calls. You can remove most notifications with the right Focus, but not notifications to control playing music/video apps, for example, nor any other widgets you happen to put on your lock screen.