Canada has a National Bank, but I don't know too much about it. (EDIT: My mistake. As bgritzut points out, this is actually their Central Bank, not a national bank that serves the public.) Personally I think a National Bank might be an ok option while retaining private banks, but IMO most of these problems are actually political ones. Lobbying is how our banking system gets the leeway to behave badly for profit. Repeal of Glass Steagall is a prime example of this. So many problems we have with corporations are actually symptoms of a corrupt political system. Money buys legislation these days, and corporations have the money and the motivation to get laws passed in their favor. Banks have plenty of money, of course. That said, I think technology might enable a more efficient system of loans and investment, whereby crowd-sourcing cuts out much of the middle management.
Technology might indeed provide solutions (like bitcoin), but we cannot hope for miracles. Technological advances are mostly stopped by politicians. It is a bit like the recent SOPA, PIPA and ACTA. They are designed to stop or even undo technological advances. Unfortunately, lobbying is effective for both the good and the bad causes, especially when you have a lot of money, as you say. A bank without money ain't no bank.