If I understand Persona correctly, you are entirely welcome to have the bank keep your cell phone number on file instead of your landlord's number. You only need to rely on a landlord if you don't want to go to the trouble of carrying a phone of your own.
If you meant I can setup my own Persona auth server on my "own" domain, then it's just that my landlord is my domain registrar. It's probably less likely that one would be stripped off "their" domain name than of "their" email account, but the problem still remains. The fundamental principles don't change in this scenario - none of credentials are in your direct possession.
If you meant that Persona consumer site can consider Persona to be not an identity but a credential, and ask me for a secondary one (2FA), then you're right. But the question on why need a landlord as a part of authentication protocol remains open.
Ah, I see your point now: my cell phone carrier can still trick the bank into unlocking my safe deposit box.
But can't we do something similar for every possible system? By controlling my computer's OS, Apple could in principle have a copy of my GPG keys and passwords right now. Ok, I'll use Linux... but do I need to worry about Intel recording the same data somehow? The point is, I'm constantly being forced to store my credentials in someone else's hands.
Well, not really. You could build your own HSM, that would store your keys and sign things for you. Obviously, only with your physical permission (a button press or even a PIN entry).
An AVR (like Arduino) would suffice without much need to trust hardware vendor. It has no communication channels except for the one you define (and you can and should define quite a restricted one) and not much die space (and too low cost) to have a backdoor to begin with. (And really paranoid ones could always go with TTL.)
The only serious problems are cryptographer-vetted RSA implementation that would fit in an AVR and writing a PKCS#11 driver for such HSM.
Yeah, this is totally on tinfoil-hat-grade paranoid side of things, but a CPU-level backdoors are not far from that.
