I remember something like this coming up before, and what I said then is still relevant. There are lots of examples throughout the world of non-corporate models for banking. And in a world where access to financial services is more or less essential, leaving this completely under corporate control makes no sense (unless you happen to be making money from the arrangement).
Also, with so many other things, a public bank to encourage the development of a community and a nation was such a good idea, that it was rolled out in post-war Germany, and never implemented in the US and UK.