I can’t think of a single instance where an essential service has been privatised and the customer has been better off because of it, and the postal service falls within the definition of an essential service.  If you don’t believe me just take a look at your next electricity and water bill where you are now paying more because you are using less.  That is because the private sector determines price, not on the basis of what gives rise to a fair profit.  It determines price on the basis of what the market will bear which, which is a sanitised term for profiteering.

Other things you may want to consider are. 

Because it is Statutory Corporation (a Corporation created and protected by statue), the way it conducts its affairs falls with the principles as provided in decisions such as Harbord v Robbins.  That is they cannot conduct themselves in a manner which is in pursuance of their own self interests, which is what private sector companies do. 

Because it is a Statutory Corporation its affair are subject to parliamentary oversight (Senate Estimates and Ministerial) and if memory serves, the CEO of Aust Post is due to appear before the Senate Estimates Committee in the near future. 

Finally if you have an actual dispute, if AP was privatised, your only recourse would be to seek a resolution in the civil courts.  However as it is a Statutory Corporation you have an alternative, and free, dispute resolution process via the Ombudsman.

So if you have a problem with the way Aust Post is conducting itself, make the issue politically sensitive. Write to your local member.  Write to the minister.  Write to whichever Senator from your State is on the Senate Estimates Committee.  Write to the Ombudsman.