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).