The anomaly of the Australian voting where a majority of votes is not needed to get a majority in the House of representatives to form government.
That is bullshit. Preferential voting
ensures that the party with the most votes gets the most seats in both houses. The system is certainly fairer than the First-Past-The-Post setup.
That is not necessarily true.
Australia has 151 electorates, of roughly (but by no means exactly equal) size. If party A got 51% of the vote in 76 electorates, and 0% of the vote in the other 75 electorates, it would form majority government but have nothing like the party with the most votes.
Now,
that would be anomalous.
There actually have been two occasions in the past 18 elections where the government was formed by whoever trailed in terms of distributed votes, but the margin was fairly low. In 1990 Labor formed remained in the driver's seat despite trailing by 0.2 percentage points. In 1998 the conservative coalition did likewise despite trailing by 1.96 percentage points.
(Link to data)
In the 2022 election, the LNP coalition did, in fact,
get more first preference votes than Labor, 4.2m vs 3.9m
As you agreed, preferential voting is preferable. Winning the most primary votes does not determine which party gets to form the next government, nor should it. The party with the most two-party-preferred votes does, and rightly so.