That's not all bad. Fractional reserve banking moves some decision making power concerning expansion and contraction of the money supply closer to where the customers are. That is inherently going to cause more volatility than a centrally controlled system. I think you'll agree though, that in most areas of human endeavor, decentralization of control adds responsiveness to local conditions and an ability to react more quickly to change. The increased volatility probably means that the right things are happening sooner, i.e. larger numbers of smaller adjustments instead of the quarterly announcement from Mt. Olympus.
Higher levels of fractional reserve banking also weaken the ability of the Federal Reserve to mess with the reserve ratio at all. In theory that ought to be one of the Fed's most powerful tools for managing the money supply, but in fact they hardly ever touch it. With a 20% reserve ratio, even a tiny change causes such a huge swing in the money supply that forecasting what will happen if they move it becomes almost impossible. So as a policy tool, it's become worthless. A cynic might suggest we leave it that way.
What makes it inherently unstable is the relationship between liabilities (which are deposits due on demand) supported by assets of a longer maturity. My reforms would require/encourage a closer matching. Then, and this is the important part, when such enterprises fail, neither depositor nor the bank is rescued. Failures will be less frequent due to the injection of reality into the banking equation.