You mean physically? Plenty of banks (especially online banks and investment banks) don't physically store any more cash than something like a jewelry store. Physical storage is hardly a core characteristic of banking; I've never been to a branch of any of my current banks. If you don't mean physically, I can't see how this is different than "have accounts"...
> Banks have accounts, right? Does bitcoin have accounts?
An account is just a ledger of credits and debits coupled with some form of access control. How is a bitcoin address meaningfully different from an account? Keep in mind that not all accounts are interest bearing, and it's very possible (even common) for one individual to have multiple accounts.