Sorry but that is not diversifying. That is what many people who invested in Finance companies did, by spreading the risk across many finance companies, and one by one they mostly all failed, as they thought they were diversifying and spreading the risk, when they weren't. Once one bank fails, it is likely that others could follow as you get a run on banks as people get nervous. It is all about perception, which is why the government brought in a guarantee last time.
What this does show though is to use one of the big four banks to keep your money, as the government will most likely bail out the big ones, as they will affect the most voters.