Coupling un-alienable, (purposefully) unchangeable biological marks to any account is always horrible idea. And not just the privacy part, for one, it can (only) be unwillingly altered (eg. by an accident), the same way as fingerprints, so a secondary backup code is needed anyway, making the whole setup a bad sort of convenience feature. The proper solution would be a safe hardware key mechanism.
If you walk into your bank and want to withdraw a large sum from your account, someone at the counter looks at your face and a shitty small photo taken from you either on their system or on your passport to determine if there is a "face match".
A proper technological solution to the current more insecure human verification process of your biometric is only an improvement, not a horrible idea as you suggest.