There's nothing wrong with a bank, just banks connected to a federal reserve of some sort?
24/7 private vaults for example is a 100% anonymous bank.
Why not develope a BTC vault?
The need for a BTC Vault is the same need for Private Security Boxes nowadays. Precious metals, important documents, or money are safely stored away from immediate access by the owner. There's a demand for it. With the plus side of the bank not being able to open it and sneak inside.
I'd consider a BTC vault/bank for part of my coins, not all of it, if some criteria were met:
- Away from my immediate access;
- Away from bank's immediate access;
- Some clever scheme where we split a private key, or use a M-to-N transaction everytime I want to make a transfer from my savings account;
- The client cannot lose the client-key (or the coins become inaccessible), but several not so secured copies can be made since physical presence is required;
- The bank cannot lose its bank-key, also (reputation, insurance);
- Neither of the parts can move the funds alone. Just the client or heirs, in any physical branch of the bank; (client-key + bank-key released by physical presence = private key)
- If the bank loses the bank-key, the client can prove that still has the client-key with a signature, and the bank would be accounted (reputation);
- If the client loses his key, the bank can prove with a signature that still has the other part of the key, and can't be accounted for the mishappening. Possibility of insurance resides on the bank's ability to safeguard data. In a disaster scenario for the bank (database leak), the losses would be mitigated by orders of magnitude, since the attacker needs the keys of all the clients in order to transfer funds.
If bitcoin becomes too valuable maybe we will see some kind of this proposed scheme.