Don't banks fill an important role by allowing people to take out loans and so increasing people's capacity to invest in their businesses, buy houses, etc? How will Bitcoin replace that role if there's no third-party to store people's money, deal out loans and charge and distribute interest?
I'm sure this has already been covered somewhere but I haven't come across the answer yet.
I'm not sure that lots of the answers here address the question.
If you are asking, how can a bank worth without fractional reserve banking, I would say that is can't really, or at least it would be very different.
A bank has no incentive to lend 500BTC to someone to buy a house, when they will only receive 500BTC back. Given that sometime inflation of the BTC supply will be zero, they could not charge interest as the money simply wouldn't exist if this was repeated around the world. As fiat money at the moment is debt, it works with the fractional reserve system, if the whole world used Bitcoin, it wouldn't.
Islamic banks as far as I understand would work with Bitcoin, maybe that would be the future..
You believe that interest can not be paid on BTC because there is no money volume inflation. This is bogous, and some misinformation about what interest is, is spread on the internet. The loaner has to get the interest from somewhere else, if it is for an investment, the profit, or if it is private, future work income.
Fractional reserve will certainly exist in a future bitcoin world, but it is risky for the depositors and that will become appearant when some bank collapses. It will have to be held back by the market, just as it is held back by regulation now. If there is going to be a regulation, the reserve fraction should be regulated. If you ask me, it could be plainly forbidden, but some genius would find a way to do it.
Islamic banks are no solution. They try to hide the interest part of the loan. The islamic ban on interest can not work, noone would lend, or lending would be a gift. Works only between friends and family.
Bitcoin is just money, and it would work like your familiar money. Still, the soundness (hardness) of the money will have profound consequenses.
I don't think you are describing the Bitcoin that Satoshi wanted or made.
If there is fractional reserve banking, to allow bitcoin banks to make loans with interest, leading to banking collapses; and if Bitcoin is just money like our familiar money, then why not use Paypal on your mobile or Apple pay?
Bitcoin is supposed to be different, not just a new replacement currency in the exact same crappy mold of the current ones.