Some clarification is necessary here:

1. Many economists and others believe that the term "fractional reserve banking" implies some sort of mechanical money-multiplier function between central bank reserves and commercial bank deposits. This implies that there is some (indirect) limitation on the amount of money banks can create when they make loans and purchase assets. This is the picture given in almost all economics textbooks. The economics textbooks are wrong, and this has been empirically proven in the 2010 Federal Reserve paper "Money, Reserves, and the Transmission of Monetary Policy: Does the Money Multiplier Exist?" (https://www.federalreserve.gov/pubs/feds/2010/201041/201041pap.pdf). There is of course still a fraction of reserves compared to deposits, so the current system is a fractional reserve system, but it is not the fractional reserve system described in economics textbooks.

2. The article by Ron Rimkus above appears to give the impression that banks fund their loans and purchases from the deposits of their customers: "commercial banks may be forced to lever up through third-party funding sources (not deposits)." This could be interpreted to give the impression that banks are intermediaries of money. The fact is that banks are the creators of deposits when they make loans and purchases*. While it might look like banks source most of their funding from customers' deposits when looking at a bank's balance sheet, this is not what happens. This important point has been authoritatively made in the Bank of England paper "Banks are not intermediaries of loanable funds — and why this matters" (http://www.bankofengland.co.uk/research/Documents/workingpapers/2015/wp…) which uses standard macroeconomic modelling techniques to show that banks' creation (and destruction) of money results in much greater instability in the economy than would otherwise be the case.

* Banks do borrow reserves from other banks via various (mainly short-term) financial instruments, and likewise from the central bank, but this is merely to enable them to settle their payments to other banks arising from their loans and purchases, (generally) not to directly fund those loans and purchases. Banks also have bank accounts with other banks, and can settle some of their payments using these accounts (in effect using the other banks' reserves).

3. The article by Ron Rimkus above appears to give the impression that under the Vollgeld Initiative, the government would be funding bank lending: "commercial banks will each be beholden to a singular funding source (i.e., the treasury)." This is incorrect. As noted already by Emma Dawnay in her comment above, the main source of banks' loanable funds would come either from a bank's own customers in the form of savings and investment accounts, i.e., the system that is in current macroeconomic models (but is currently wrong), or from other bank's (or other financial institution's) customers, via the inter-bank lending market (or from selling bonds or shares). Any lending to banks from the central bank would normally only be for fine-tuning and "last resort" purposes (as it is supposed to be now, but isn't). This would put banks on a level playing field with insurance companies, investment banks, and other financial intermediaries, and since banks would no longer be able to create money to fuel short-term speculation, the whole financial system would become more stable as well. One would think that financial intermediaries would welcome being able to compete on a level playing field with banks.

4. As referenced in point 2 above, the standard macroeconomic analyses (used by central banks, the IMF, etc.) show that a monetary system like the Vollgeld Initiative would actually tend to reduce instability. With regard to buffers, the IMF paper "The Chicago Plan Revisited" (https://www.imf.org/external/pubs/cat/longres.aspx?sk=26178.0), cited in the comment above by Joseph Pijanowski, explains how capital buffers (and interest rate policy) would actually become effective macro-prudential tools (they aren't currently, because they don't effectively limit banks' pro-cyclical effects on the economy).

In conclusion, based on the empirical and calibrated analyses referenced above, there appears to be no rational reason to fear the proposals in the Vollgeld Initiative.