I have seen a variety of banks allowing access to their remote banking environment with just your fingerprint (via iphones and similar devices). Are these valid examples of a wider group of cases where pure biometric authentication is acceptable, or is this just a failure of the banks in question?
I am of the school of thought that Biometrics are NEVER acceptable to use as the only authentication method, you leave your Biometric data everywhere, it is almost a security paradox. I can lift fingerprints off of your keyboard, car, or elevator panel, I can make a voice recording of you, I can take your picture, get your face off a security camera, and I am Bad Guy Bob - I will jump you at your car and cut off/scoop out whatever I need.
Some other examples/articles of people who think BMs are negligent to use:
You also have to realize that there is an error-of-margin built into these Biometric security solutions, all it takes is for your to roll your finger on the scanner wrong or squint with a retinal scanner for it to scream at you and say ACCESS DENIED - making them easier to defeat, and unlike changing a password, or salting a hash, you cannot change your fingerprints easily nor change your retinas - once you are compromised, and use biometrics extensively, there is no way to quickly change.
Using only biometrics for authentication is a bad idea, as have been said many times before. So the answer to the question "when to use only biometrics" is never or at least not if you are protecting anything of value. You can use it if you only want identification, and not authentication - i.e. if you had been fine with replacing the finger swipe with a text box and the instruction "enter your name here".
If people use biometrics only in other situations, e.g. banking, it is because they are either incompetent, lazy or just don't care. However, biometrics can be a part of a multi factor authentication scheme, where your fingerprint represents "something you are".
Actually, the example you give with banking on an iPhone is probably an example of this, where the phone - "something you have" - is the other factor. I am asuming here that you can only use your fingerprint on a phone that you have connected to your account.
However, it is not a very good 2FA, because the likelihood that the first factor being breached if the second factor is breached is quite high. Think of your spouse using your finger on your phone while you sleep.
However, if there is a PIN - "something you know" - on the phone suddenly you might have three factors. But the bank can't know if you have a good PIN on your phone or not. If I was a bank, I would want a passowrd for the banking app as well.