First of all please let me take a stance regarding fractional reserve banking: accepting deposits, putting a fraction aside and lending out the remainder is the standard way any and all banks operate, regardless if they use gold, green paper or bitcoins. The notion that fractional reserve banking is somewhat only possible if enabled by a central bank is a Zeitgeist conspirationista type of fallacy.
Any and all banks is a very strong statement. There are lots of other services banks offer.
Only a central bank issued paper currency allows such a bank to guarantee its deposits. Under hard money, maturity mismatching will result in the bank failing.
An honest bank can offer current accounts for a fee and time deposits with interest which is then lend out as fixed-term credit. It can also offer brokerage services like the ability to buy bonds directly, with all associated risks and benefits.
A hard currency will prevent moral hazard and make it simpler for customers to actually understand what's going on. What's wrong with that?
Fractional reserve banking is popular, because it makes people feel richer than they actually are, but this leads to lots of problems like too cheap credit, malinvestment and capital consumption.