Biometrics may help solve a problem but they also create a new one.
Tying account access to one small, portable, highly vulnerable device with questionable reliability is an inherently bad idea in my opinion. Lose access to the device for any reason (lost, stolen, dropped, the fingerprint reader fails or the phone simply dies) and you also lose access to your account.
I prefer to simply create decent login credentials and store them only in my head --- not in a app and not in a web browser either. This way, when (not if) my phone stops working, I can immediately switch to an older backup phone without missing a beat.