The Bank is backed by the full faith of the State and the tax payers are the beneficiaries on any profits of the bank as they are ploughed back into state programs that otherwise would be funded by taxes.
Private ownership is a good thing but may not always translate into wealth distribution subscribing to the principle of equity. The case of North Dakota Bank in the United States may not necessarily be the best example in this context but certainly it presents a plus point of having a state-owned bank. Our own case brings forth the rationale because in not divesting everything, we do no discourage other players in the financial market from operating. The presence in fact allows for interventions to the benefit of communities needing such attention.
Then again this is probably one side of an argument that may be more complex than appears to the eye.