The banks provide a service that has some intrinsic value: They protect your cash better than you can, and store it in a place that is physically separate from your home.
Home thefts occur with a higher frequency than bank thefts, and someone who's known to keep large quantities of cash in there home becomes a bigger target. If your money is stored in a bank, you're more exposed to a banking system collapse but insured against ordinary theivery. If your home is destroyed, then your money is still safe; if your bank goes bust you still have your home (or at least the things inside it).
In this case you have to pay a small fee, but you decrease the amount of cash that can be used for loans, and thus make loans more expensive, leading to better rates for lenders in the future. (At least this is my understanding at the moment - still getting into the topic, so please excuse if I am oversimplifiying.)
Why with cash many don't do that, beats me. According to Keynes, people should withdraw their cash when there is no interest to be gained ("liquidity trap"). In practice, people don't, and that makes Bitcoiners crazy: good marketing makes (especially badly informed) people act uneconomically, since they think they are saving, while they are actually investing in an indifferent manner.
Other important aspects of Bitcoin are, that it makes the money supply transparent, and everybody can validate transactions. This is not as simple with cash or gold.