There is nothing inherently wrong with fractional reserve banking, provided the parties who enter into such an agreement understand the agreement, and assume the risk.

The problem is a state-sponsored fractional reserve system where bank notes are enforceable legal tender, deposits are insured by the Government, and banks are not allowed to fail. This creates all kinds of moral hazard, market distortions as well as inflation.

Fractional reserve banking as occurred during the decentralised "Free Banking" era in the US (1837 - 1864) - i.e. subject to proper competition and where the risks are assumed by those entering into contracts with each other, not third parties - is healthy and desirable. During the Free Banking era, bank notes were not enforceable tender, and often traded at a discount against Federal notes the further they traveled from the issuing bank.

One of the major benefits of FRB of this kind is the supply of credit not being limited by the available supply of money. If people are willing to accept a Bitcoin bank's "money" as payment it can also issue credit, which can fuel investment in the bitcoin economy. The important point is that banks which issue credit (e.g. money) improperly by lending to untrustworthy parties, businesses which aren't viable, or into property bubbles, go bust. This imposes discipline on the banks.

If bitcoin is successful this will almost certainly happen, and it will be beneficial for a number of reasons as stated by Hal and others.