Fractional reserve banking is unstable without a monopoly over the ability to print currency, due to the >0 possibility that a bank runs out of reserves.
That's like saying: "Gold atoms are unstable because quantum mechanics tells us that there is a >0 possibility that they will spontaneously decay."
Yes, in the very very very long run the universe will suffer heat death and there will be no gold (or any other atoms) left.
If the probability of bank runs is very small, then fractional reserve banking works. Or, in other words, if banks can establish and maintain trust in their ability to repay deposits they'll be stable even if they practice fractional reserve banking.
I hope we'll eventually find out the hard way if, or which, Bitcoin banks can establish and maintain trust.
Not true. If I deposit 100 bitcoins at a bank, the bank lends out 90, and I want to withdraw my 100 bitcoins, the bank is screwed. Even if they lend out 25, the bank is screwed.
On demand deposits simply cannot be loaned out if a banking system is to ultimately remain stable. Sure, some banks can try to do it, but then they better not call them "on demand deposits". Deposits can be loaned out, but not with a guarantee of redemption. That is simply impossible as Bitcoins cannot be created out of thin air.
So long as on-demand deposits are not loaned out and time deposits are loaned out, we're fine. Alternatively, on-demand deposits can be loaned out, with a "maybe" promise of repayment. Try and see who will go for that
You might call this fractional reserve banking, but then we're just arguing over semantics.