Banks can still make loans simply by offering certificates of deposit. This is the above-board way of loaning out people's money -- you make it absolutely clear that taking it out early has a cost, because the money is locked up in (hopefully) profitable ventures.
Would that be less profitable for the banks? Not really -- they would just adjust their prices to compensate, by charging fees on idle money that's instantly redeemable.
And if you let a secondary market for CDs flower, customers can still get good liquidity. Just in a way that's better subject to market discipline.