If banks had to be non-profits, private citizens would invest their own money. Then these private citizens would license their money to private citizens or organizations for that purpose (to avoid the hassles of doing it themselves). Which is essentially the system we have now.
Unless you're talking about splitting investment and commercial banking.. Look into the Glass-Steagall act.
Unless you're talking about splitting investment and commercial banking.. Look into the Glass-Steagall act.