A year later the borrower pays back the loan by turning in 91.8 bitcoins to the bank.  I withdraw 101 bitcoins from the bank and the bank ends up with 0.8 bitcoins profit.  Is there something wrong with this scenario?  Is it any different from conventional currency?>

What you described is bank using FRB, which won't work in the long run.
The question is you need ask. What will happen when you try to withdraw your 100 bitcoins from such bank, but the bank has only 10 of them, because the 90 has lent?
There are few lessons:
1) Such bank can't afford to keep lending your bitcoins, because there is no cental bank which would create the missing bitcoins on demand;
2) In reality there is always 100 of bitcoins, never 190, and never will become 190 again because no central bank can print the missing 90 bitcoins.


What I say the banking of BTC is fully possible, but shouldn't be based on FRB. It should be 100% reserve banking. People don't understand the concept of 100% banking because currently the FRB is enforced by governments all over the world.
With 100% reserve bank, there would be no interest to earn. Because it would be a true bank, more likely you would pay fees for storing your bitcoins there. The benefit is that the bitcoins itself would no lose value, and would always appreciate in long run, thus keeping your savings safe.