No solution is airtight, but if it makes it better for 10% of users without making it worse for the other 90%, it seems like a good idea.
Adding a visual indication of a secure dialog can at least help the power users, while not changing anything for the ones that don't know the difference.
EDIT: Oh sorry, I seen what you are saying now - entering password into the phrase field. Instead, just make it an image that the user selects, or even creates.
"You didn't notice one of the dozen popups asking for credentials lacked your magical hidden phase YOUR FAULT!"
If Apple were going to explore a strategy to fix this, they would likely be better off redirecting the user out of the app before asking for credentials, or prompting them in notifications/home screen only.