So, on the surface, they hold on to the excess money of the rich and lend it to the poor, which sounds a good thing, as it's taking a resource from those that have more then they need and sharing it with those that are short.
However, given these are large companies, their main focus is profit. They need the money from the rich to invest to do this, so they need to encourage the rich to leave it with them and hence pay them a small fee for this and likewise charge a fee for loaning to the poor.
The result being that although there is a temporary flow of money from rich to poor through the bank, the longer-term flow of money goes the other way from those that need it to those who don't. In effect, we seem to have built wealth inequality amplifiers and placed them centrally within our society.
OK, things are a bit different with the co-op and building societies, but they're much less influential to society as a result. You just have to look at the number of the later that demutualised to in order to compete to see that.
There's also North Dakota with it's state owned bank (rather than one the state is bailing out). Although there seems to have been some interesting ideas behind it's setup, as far as I can see it doesn't actually do a lot other than focus it's loans and investments on local industry.
All in all, banks seems a bizarre idea really. What could be a useful public services have been forced into being profit hungry monsters in order to survive.