Another scenario is that banks co-opt Bitcoin providing "wallet security services".
Dont get me wrong you can still start new "banks" for bitcoin but they will be different.
I expect whole swathes of the older generation will never choose to switch to the Be Your Own Bank model, computers are terrifying enough as it is without being given the ability to delete your life savings. I'm currently picturing the look on their face when you say to them "But you can back it up in many safe and secure ways!". Forcing their hand with ginormous economic calamities is the only way certain over-the-hill conservative refuseniks would ever switch.
That is the unavoidable truth of an "account" not bound to an identity. There are plenty of banks that work the same way where if you lose your account details just showing up and saying "Yo! I was that dude that opened a vault/account here but I forgot my access" will not be enough.
The real question you should ask yourself however is not what if your local data gets erased.. but if you will have local data in the first place? There is a reasonable chance that people will be moving in the direction of cloud storage where your data would be keep secure by the internet.