The private key and wallet would still exist, but transactions would not be validated until you processed your key against whatever encryption algorithm thereby proving the owner of the wallet made the transaction.
As I said, addresses are already keypairs. If you need to supply a key to actualize a transaction, the private key corresponding to an address is that key. Multiple such keys don't increase security (although it could add new functionality, like escrow transactions). Either I still don't get what you mean, or you need to check this: https://en.bitcoin.it/wiki/Address
(i.e. wallets don't have "owner"s).
Think of it this way, each address is itself a wallet in the sense you use. Bitcoin client creates a new address for you to receive the "change" from your transaction. You could modify the client to not create new addresses and use only one. Then you can keep your "single" private key offline, even in your memory, or a combination of that. But then, you do not have to use a wallet file at all. Wallet file is just a convenient store of your private keys, it doesn't even store your "balance".
That way any banks or holding houses wouldn't be holding the chance of losing everything, because in the worse scenario after being hacked, you'd just create a new wallet, transfer funds using your key and be right as rain.
If you won't transfer all required information to make a transaction on your behalf to the bank, there is no need to use a bank at all. That's actually the beauty of the protocol.