HIPPA exists and has a lot of teeth. Given this extensive liability, I trust that if anything does go wrong they will be punished. Recordings might dramatically improve patient outcomes, and so I will let them
Even pre-existing insurance denials could return in the US.
Don't let systems record what they don't need. They aren't your friend.
HIPAA has laughably vague rules. It's not protecting much, and you probably have better protection through tort law wrt your private information.