Banks couldn't lose depositors' money. Deposits would be safeguarded in a mutual fund that holds nothing but cash. Withdrawals would be via check or ATM, as now.
Banks wouldn't be exposed to loan losses. All loans would be made by mutual funds using money raised from investors. Those investors would swallow any losses from defaults.
Insurers couldn't be ruined by big claims. Policies would be issued by a mutual fund that collects insurance premiums. Payments would be limited to whatever is in the fund.
These would become pure advisers. They would be banned from holding assets or borrowing to buy them, so they would not be exposed to market losses.