Maybe people should have the option to save their money in a bank that doesn't loan out their savings at all? Does such a thing exist? I would be willing to pay

Maybe people should have the option to save their money in a bank that doesn't loan out their savings at all? Does such a thing exist? I would be willing to pay a flat monthly fee to keep my money in a bank and use their services in lieu of receiving their paltry interest on my savings account, in exchange for the knowledge that they actually have my money. I know this system of massive loan-to-deposit ratios is conducive to economic growth, nevertheless I get the impression we're all being scammed on a fundamental level by the banking system at large- and any suggestion of meaningful change is always dismissed as if this house of cards is just the way things have to be, and always has been