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 it as Bitcoin banks. Indeed, if you consider as a bank only institutions that loan out money, then 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 either, especially banks established by large corporations specifically to process payments and nothing more. So this is not a prerequisite for a bank, at least, these days. Further, web wallets now issue payment cards which is 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 in the bank (welcome to negative interest rates). As you can see, there is not much which separates web wallets from what can be loosely called a bank nowadays