This topic has a thread before. Not even sure now why OP created another one. This has long been debated and no real winner has emerged, I think there are more people not in favor of this and those that are. This is really why there have been no real attempt to create a bitcoin bank that has surfaced since bitcoin's inception
I think this is not quite so
Web wallets can pretty well cut as Bitcoin banks. Indeed, if you consider as bank only institutions that loan out money, this is next to impossible with Bitcoin due to its devastating volatility. On the other hand, some of our regular banks aren't involved in loaning money, especially banks established by large corporations specifically to process payments and nothing more. So this is not a prerequisite for a bank, at least, in these days. Further, web wallets now issue payment cards which what most fiat banks do. They don't pay interest but in today's perverted world, banks even demand you to pay for just keeping your money their (welcome to negative interest rates). As you can see, there is not much which separates web wallets form what can be considered as a bank nowadays
I believe that Bitcoin banks should not exist at all because it does not level the very concept of crypto currency and their capabilities. When I imagine what the current banking system is doing, I do not want to do the same with bitcoin.