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
You forget to add a few ugly things
For example, that the average life span of a bank during this "Free Banking era " in the US was around 3 years (if my memory serves me correct). Surely not a good thing, by any means. Further, since gold was used as money back then, to deal directly with it was not very handy, so people used depositary receipts they received when they put their gold into such banks. Obviously, banks ended up issuing more receipts than they had gold in their vaults, which inevitably led to bank runs and chain bank bankruptcies (the word bankruptcy itself seems to stem from banks, which is not surprising). Just in case, today's monetary systems have nothing to do with FRB