It can't be fundamentally unproductive. By definition, if the bank attracts deposits and is satisfying depositors, and is loaning money to people able and willing to pay interest, then it's both productive and sustainable. And beneficial, one might add.
OTOH if they're loaning government money, based on bailouts, favors, and supports, that's a whole 'nother kettle of fish. That invites and breeds corruption of every sort, intentional or not.
Agreed that a healthy economy optimizes yield of productive activities.
ISTM things get off track when govts diddle the banks (rather than just enforce fair play). That happens for both innocent and guilty reasons: 1) idiot govts try to optimize *their* idea of productivity, which doesn't work, and 2) a positive feedback loop where bigger gov't squeezes out small competitors & makes bigger corps.
(More regs =3D> more lobbyists =3D>
more barriers to entry =3D>
more favors for big corps =3D>
more contributions to politicians who make it all possible, who hire more lobbyists, who press for ...)
-- Cheers, James Arthur