You could build a complicated banking system on top Bitcoin too, that could do things like reverse unauthorized transactions, but that would get rid of the reason some people are really interested in Bitcoin.
Right, which is the point. No one same would argue that cash is a secure form of money storage. It's got some selling points, but security is not one of them.
The other purpose a bank serves is to protect your money; A bank at it's most basic level is physical security: steel vaults doors, security deposit boxes, security processes, guards, etc. All ancillary (and highly profitable) services flow up from providing this primary need for it's depositors.
Because BitCoin relies on technology to secure your money, so long as users could find an acceptable level of security to replicate this with "high"-technology, there wouldn't be a need for traditional banks to store your money.
Only if you don't consider protection from theft an attribute of secure money storage. If somebody compromises my bank account credentials, it will be annoying and time consuming but I will ultimately get my money back. If somebody steals my bitcoin wallet, I am shit out of luck.