"You assume a zero sum where there is no evidence for one."
I am referring to systems comparable to the contemporary U.S. banking system: fractional reserve, fiat currency, government guarantee of "deposits". The first property of any such banking system is the real interest rate earned by savers (prior to government overhead) is the nominal rate minus the inflation rate. The real rate is *much* smaller than the nominal rate.
During the 1970s it was sharply negative, in other words savers lost money in real terms every year, because inflation was so high. Most of the time the real interest on government guaranteed savings accounts is one percentage point at best. Whether the the $200 billion we are churning out to sustain Fannie Mae and Freddie Mac is enough to reduce government guaranteed savings deposits to a true zero sum game is hard to say. There is no question that they are _close_ to a zero sum game.
There is a perfectly good way to accomplish what you are suggesting without fractional reserve _banking_ or government guaranteed deposits. Have individuals invest in diversified bond funds that purchase bonds issued by building societies, credit unions, and the like. People still get loans to build homes, investors earn more in real terms, and the rates automatically and properly float with the risk the bond issuers undertake - instead of as now where you earn half a percent in real terms whether your bank is about to go under or not, which is a very high price to pay for a taxpayer guarantee.
Poorly managed building societies might fail (affecting the return on bond funds), but the commercial banking system as a whole will be immune from systemic failure, because true _deposits_ will no longer be lent out, but rather only the proceeds of what are in effect loans to independent lending institutions, with the risk widely distributed, instead of concentrated with those so unfortunate to make a direct loan to a bank and/or the taxpayers that guarantee whatever crazy scheme the banks will cook up next.