Fractional reserve banking would be MUCH harder to do with bitcoins than physical currency, unless banks were allowed to print paper money "backed" by bitcoins.
I don't understand the need for actual paper. If what you mean by "print paper money" is issue an electronic token representing a bitcoin, I don't think that's difficult to do. It's what mybitcoin.com does now - it is essentially a full-reserve bank with its own "money."
Transactions within the bank would also be possible with "fake" bitcoins, especially if all the bitcoins are held in the bank's wallet, and accounts simply have balances.
There are no "fake" bitcoins. There are just bank credits, redeemable for bitcoins by the bank on certain terms, or which can be used for payment or sold to third parties.
A bank could create as much credit as it wanted, or its depositors were prepared to tolerate, but it would quickly go bust if it abused this privilege.
The problems start hitting hard when you try to send actual bitcoins. If the bank extends itself far enough, and has enough clients, it may be possible wipe out it's coffers with a transaction or two from each client.
True, but that is precisely why successful banks will need to be prudent. The problem with the banking system today is that the risk of failure is mitigated by government support, which creates moral hazard and reckless lending.
Bottom line, you CAN do fractional reserve banking with bitcoin, but it requires that every other bank and customer agree that your paper or digital notes are as good as the bitcoins they represent, in order to pull it off without any hitches.
It doesn't require that
everybody accept the banks' notes, just that there is enough demand for those notes.
They don't have to be "as good as bitcoins" - there's nothing to stop third parties buying up bank notes at a discount to their face value. The risk of the bank collapsing would be priced in.
I agree with you that it's risky - but the market will impose discipline on the banks, to stop them taking excessive risks, remove ones which do, and reward those that don't. Meanwhile depositors will be able to earn interest on their savings, and secure their wallets from theft.