You can go into Settings > General > Restrictions and turn OFF the ability for any app to be deleted. This will be universal, in that any/every app will be stopped from deleting. And, you won't get a password request whenever you try to delete an app - you'll have to go back into the Settings app and remove the restriction before you can delete anything.
But, it'll prevent the deleting of apps, so maybe it'll work enough for you?
Marilyn