While reading the answer to Implications of abolishing Fractional Reserve Banking on mortgages and interest rates, I started to wonder if there wasn't a simple solution to the problems that would arise with the introduction of a constant money supply.
Right now, banks create the illusion of more money existing by accepting deposits and holding onto only a fraction of them while lending out the rest. Alternatively, could they not just package up loans into investments and essentially sell shares in the investments to average people. This would essentially have the same effect, your cash would be tied up in the bank and you would receive some amount of interest on it. The investments could even be structured and insured in a similar way to the current system in order to maintain some amount of liquidity. The only big change is that people would be very much aware of where there money is when they put it in the bank, which to me would only increase the robustness of the system and reduce the possibility of bank runs, as there would be a general understanding that some of your money is loaned out at any given time.
Has this idea been studied, and are there any known or obvious flaws that I am not seeing?