Seven benefits of a public post office bank
A public post office bank can transform Australia, just as the original Commonwealth Bank did after it started in post offices 110 years ago in 1912. This is an economic policy solution which all Australians can get behind, and which will have a far-reaching positive impact. Here are just Seven of the benefits: (Click on a banner to expand)

Australia Post is mandated by the Australian Postal Corporation Act 1989 to provide mail service that is "reasonably accessible to all people in Australia on an equitable basis".
No discrimination—As a public institution, the postal bank would not be allowed to discriminate against particular businesses or individuals, which means no lawful customer would ever be "de-banked".

That means the post office bank would not default on deposits, nor would your deposits be in danger of "bail-in".
This model would be very similar to the way post offices were the first branches of the original Commonwealth Bank when it started in 1912, but it would be permanent. The model would ensure banking services to all communities, and the ongoing economic viability of Australia Post's branch network.

A June 2019 Reserve Bank of Australia paper on cash accessibility noted that "Australia Post's Bank@Post service is the only in-person banking facility within a reasonable distance for many Australians living in regional or remote areas".
Source: RBA – https://www.rba.gov.au/publications/bulletin/2019/jun/cash-withdrawal-symptoms.html

Loans would not be assessed on whether they maximise the bank's profit, which is the culture that has motivated private banks to chase reckless mortgage lending. The postal bank would not engage in derivatives trading or other forms of speculation.
Operate in tandem with a national development bank—The post office bank could invest any surplus funds in a national development and infrastructure bank—this investment would also be fully government guaranteed.
A national development and infrastructure bank could then put those funds to work in the development of infra-structure and industries that Australia needs for productive economic growth and prosperity.
Australians who deposit their savings in the national post office bank would therefore know that not only are their savings safe, but they are being used for the economic development of Australia.
A public banking alternative would force the private banks to compete on all fronts and lift their game, thereby helping to raise banking standards.
If the private banks persist with ripping off and exploiting customers to maximise their profits, more and more Australians will turn to the public banking option which, while it would make modest profits, would exist primarily to provide a service.