Keep in mind that what allows fractional reserve is lack of competition (a company could profitably differentiate itself from competitors by maintaining transparency), and what causes lack of competition is government regulation. In a completely unregulated market, fractional reserve is a non-issue because there is no possibility of monopolistic privilege for any one company or cartel.
Fractional reserve banking exists in a competitive environment and has always done so. So that premise is faulty.
If there is a market for fractional reserve banking and derivatives in Bitcoin, all is well. If not, its still a useful way of doing business privately. I suspect that FRB would push up the price of Bitcoin as it would create demand for proven reserves and banks can't fudge a Bitcoin reserve.