> Money that is "saved" can still be used for productive purposes.

If I wanted to put money to productive purposes (at risk, with reward) I would do so myself. I'd buy bonds, stocks, options, lend money out, whatever. I already do this.

Whatever I keep in cash, without investing, is intentionally kept as cash, and I want that part to be zero risk, I don't need the bank to help me invest it at nonzero risk.