Why would you want Bitcoin to function as a regular bank? More important, what is Bitcoin according to you missing since you want it to be like a bank? You can send and receive money 24/7 instantly without the need of a middle man, you own everything in full, it's a great tool to avoid interferene from banks and governments. Only benefits. That's why I don't understand what you are missing. Or probably.... You are not getting any interest on your coins as it is, is that what you are looking for?
Of course I am well aware of the problems that people are facing when looking into certain lending sites, but if you don't like what they offer, you can start your own lending service.
The lending subject was just an example. Everything you "can't" do with Bitcoin, can be done through various other ways where you don't need an entity naming itself a Bitcoin bank. It's an open market. Everything is available.