Banks have time deposits that need to be shifted to demand deposits. Stop paying interest on the many types of accounts and let the money flow through the non-banks.
Non-banks are true intermediaries. Savings kept at commercial banks would flow to non-banks which does not diminish the commercial banks in anyway. The savers money becomes the non-banks money and the non-banks keep their money in commercial banks. When non-banks make investments or loans the recipients of the invested money and the loan proceeds keep that money in the commercial bank. And so on. Commercial banks maintain the same amount of deposits, it is just the time deposits now become demand deposits.
It is actually weird that banks collectively pay interest on money they already own, anyway.
One of the most important non-banks is insurance companies. They make construction loans. Savings accounts at banks are inert. They just sit there doing nothing. Banks do not and cannot lend out their deposits. Instead, savers putting their savings in an investment product from an insurance company will result in a constructive use of the savings. An insurance company is an intermediary between savers and borrowers. Commercial banks are not.
If you provide you savings to a money market account at Ally bank a car loan will be funded.
Hedge funds invest in many different areas. Equipment leasing companies provide financing for production equipment. There are broker-dealers. There are mutual funds. Mortgage companies. Private equity funds. Corporations offer (used to and will again) commercial paper. Merrill Lynch is an investment bank. So is Goldman Sacks. You can buy securitized products (which pools your risk). Accounts Receivable lenders.
Eliminate taxes on investments in non-bank products at the same time you eliminate interest paying products in commercial banks will cause a massive outflow of savings from commercial bank savings accounts and into non-bank useful investment.
Remember, banks have no reduction in their deposits. There is no destruction of money.