First. With the current system, the IOU that you get from the bank is indistinguishable from the currency. Say you deposit 100 USD in BoA account, the bank will show that you have 100 USD, not 100 BoAD that are redeemable 1 on 1 with USD. So, that's a big difference because that will mean we need another form of currency to make BTC currency work, right? Name it banks' IOUs, vouchers, litecoins, etc.
No we wouldn't need such an alternative currency, but one could exist.
No, you're getting confused. We already have rudimentary banks, in the form of online wallet services. Imagine if one particular service, let's call it BitcoinPal, were to grow large enough that it had thousands of consumers & retail websites with accounts. Whenever a consumer used his web portal or smartphone app to import the address of a member's retail website, the computer doing the action could recognize that address to belong to a member, and simply credit that member's account. This would require group storage of bitcoins, like a bank does with cash, and thus there would be some currently unmet need that the bank can provide that is costly to an individual consumer. Most likely this would be transaction fee reduction, as thousands of members could operate in this way (so long as the banking institution was trusted) and only produce a blockchain bound transaction. Such transactions are cheap now, but they are subject to market forces too. When Bitcoin is seving as many transactions per second as Visa, we can't expect a transaction fee to still be a nickel.
I still don't understand how a loans with interest system will work in a BTC based economy. Knowing that BTC can not be created by banks via "credit expansion" and that there is a limited number of them in existence, how will the interest be paid back? With what BTCs?
Ah, I see the block. You belive that successful banks would eventually own all the bitcoins, correct? Well the free market doesn't work that way, those bitcoins, including the interest, is always in motion. Banks pay employees, employees buy services, businesses pay their loans; and when they don't, loans default and banks lose both the principal and interest on that loan, and the interest on a couple others to balance out the loss of reserves. Interest rates would naturally trend down toward a point that is close to the default rate plus the dispersion rate. Very unlike our current system of fixed rates.