I think the Australian system is broken in a different way.
As a fun exercise - review the AU constitution and find all the references to the role of PM.
Sean Kelly writing in TheMonthly(.com.au) recently observed after the last election:
"It’s a mistake to think that there is such a thing as the national will or the voice of the people that is somehow expressed through the electoral process, or that an election result can be construed strictly as approval or disapproval of a set of policies. People vote in all sorts of ways for all sorts of reasons – personal benefit, an attempt at dispassionate policy assessment, preference for individual politicians, habit – and the number of votes that decide any given election is always a small fraction of the population.
"If there’s one thing this election result has told us, it’s that the appeal of both major parties is still on the decline. Twenty-five percent of voters put neither Liberal nor Labor first; yet collectively they are only represented by 3% of the lower house and perhaps 11% of the senate. (Whether it makes sense to think of them collectively is a separate question.) That’s a quarter of the country who look at parliament and don’t see themselves represented."
From a purely leadership POV, US and AU have the same problem that >50% of people don't want the leader that they have - due primarily to the fixation of a) a single leadership role (bring back the triumvirates! :) and b) two-party politics.
When you're informed you only have two choices - you're probably not in a democracy.