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.

I'm talking about all financial institutions being non-profits. Financial institutions would not have a responsibility to shareholders to show a return on investment. Instead they would only have a responsibility to provide a needed service to society (i.e. the creation of and access to capital).

It's not exactly what you're thinking of, but you may be interested in Positive Money, as it's tackling a number of the same issues (it's a UK scheme, but it's just as applicable elsewhere)... http://www.positivemoney.org/

Co-op banks address many of your concerns, and are very popular in some groups.