Do you treat your matrass like a bank? Maybe with the pidgin carrier protocol to do money transfers?
You don't hold your own money, you don't manage transferring your own money, you basically don't do any of the things a bank does. How does that make you your own bank exactly?
So that would not really constitute a bank that stores currency.
(I have nothing on crypto currencies, btw., and if it gives a feeling of agency to use them I applaud it)
If you start from there, you'll never understand bitcoin. I own bitcoin precisely because it is not what economists, bankers and politicians want me to own.