Gold mining companies are accountable to reality: they can't extract gold that isn't there. Nor can they extract gold that isn't profitable to get at given the technological context. Money is supposed to be a representation of wealth, and private banking does that perfectly.

In contrast, government banks are "accountable" only to the whims of politicians and a public that wants its cake ("reasonable" taxes) and to eat it too (immoral entitlement programs). That's one purpose that statist banking serves: to make up for the inherent, recurring government budget shortfall by printing boatloads of money, forcibly lowering the standard of living of anyone that saves, in order to "benefit" those that won't or can't.