To put it another way - when you deposit your money in a bank it is no longer your money. It is the bank’s money and you are compensated for this transformation through being paid interest - or at least not having to pay them a storage fee. In this I fully agree with Lord Cottenham in Foley v. Hill and Others (I am quoting here from Rothbard as the Google copy is not in text form)
Money, when paid into a bank, ceases altogether to be the money of the principal; it is then the money of the banker, who is bound to an equivalent by paying a similar sum to that deposited with him when he is asked for it . . . . The money placed in the custody of a banker is, to all intents and purposes, the money of the banker, to do with it as he pleases; he is guilty of no breach of trust in employing it; he is not answerable to the principal if he puts it into jeopardy, if he engages in a hazardous speculation; he is not bound to keep it or deal with it as the property of his principal; but he is, of course, answerable for the mount, because he has contracted . . . .
Rothbard, looking at Foley which clearly stated this principle, saw it as a disastrous mistake. I would agree if I were paying the bank to store my money. I am not, though. The bank pays me while they have it. Where do they get this money? By lending it out - therefore, when I deposit my money in a bank it is no longer my money, but a claim on the assets of the bank.
If what you want is a place to store your money and be sure that the money is safe, great. They are called safety deposit boxes and are available in the vaults of most major banks. Just expect to pay for their use.