There's a perspective problem here.

Australia Post doesn't make profits and losses, it provides services - and services have costs, not losses.
Expecting Australia Post to:
A) Deliver packages of international origin for free
B) To unprofitable remote/rural areas C) AND turn a profit like a business whilst D) For profit courier companies undercut them on profitable metro areas...

Well it's not going to work long term.
And post offices are more than just places to drop off a package you want delivered, lots of people use them as their local bank branch for necessary in person tasks - especially in the a fore mentioned rural areas.

Long story short, Australia Post should not have been privatised - it's an essential service and essential services are natural monopolies.

Given such an essential service, I personally don't think it's important they are turning a profit. But is it run efficiently? I have no idea and this article doesn't really go into it. Had a quick search and found Australia Post's Efficiency of Delivering Reserved Letter Services. Haven't read it in full yet but first glance looks interesting.

And from some quick digging, I found that every year their revenue increases:

2022 $8864M
2021 $8208M
2020 $7499M
2019 $6990M
2018 $6877M

From their annual reports page: https://auspost.com.au/about-us/news-media/publications#annual

Didn't the Rolex watch lady have the place running super efficiently and that is why they fired her? Or is that all conspiracy nonsense?

Public services aren’t suppose to make money, that’s what tax is for

Anyone argue otherwise meaning we should fire the whole parliament and I don’t believe they are ever profitable

This is the best summary I could come up with:

After recording a profit before tax of just $23.6m for the six months to 31 December, the chief executive, Paul Graham, had warned in February that Australia Post will report a loss this year for the first time since 2015.

These include reducing letter frequency and closing some full-service post offices in metro areas while allowing more self-service options such as parcel lockers.

The communications minister, Michelle Rowland, said “Australia Post is a cherished national and publicly-owned institution” facing “significant structural headwinds”.

“The Albanese government is committed to supporting Australia Post modernise so that it can continue delivering the essential services consumers and small businesses rely on to stay connected,” she said.

The Liberal MP Keith Wolahan, who is campaigning against closures in the eastern suburbs of Melbourne, warned that “Australia Post is about more than letters and parcels”.

The independent senator David Pocock agreed that post offices serve a “very important purpose”, including providing banking services and getting photos for ID.

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