> The waiting for the patent to expire
That's not what the Australian government does.
Even for prescription drugs still under patent, the federal government negotiating on behalf of the whole country as a monopsony purchaser can demand (and get) much bigger discounts. (A monopoly is when a market effectively has only one seller, a monopsony is when a market effectively has only one buyer.)
Whereas, in the US, each insurer negotiates separately, so all but the very largest have weaker bargaining power than the Australian government has, simply because they don't represent as many insureds. The US has over 1000 health insurers, only the top two or three (such as UnitedHealth Group) have more insureds than the Australian government has (26 million).
Plus, even though a handful of very large US insurers such as UnitedHealth have more insureds than the Australian government does, the fact that the Australian government is a sovereign state and not just the purchaser but also the regulator and legislator gives it additional negotiating clout that such private insurers lack. Also, if UnitedHealth refuses to reach a deal with the drug manufacturer, they risk losing insurance customers to other insurers who are willing to do so; Australians can't realistically switch public health insurers (moving overseas is the only real way; private health insurance usually has very modest prescription drug benefits)
> Australia would have to start funding research.
Australia actually does have significant medical research funding. Unfortunately it seems to be a struggle to find good data on exactly how much (in easily comparable terms, such as %GDP) – the WHO's statistics [0] on this topic are missing both the US and Australia for whatever reason. But even in the absence of hard figures, I'd totally believe the US spends at least double (on a % GDP basis). But I think that's part of a broader economic problem with Australian underspending on R&D (both public and private) which goes beyond just health.
The other problem I know, is Australia has largely lost its ability to productise pharmaceutical innovations (outside of certain niche areas), which means even when some novel drug is discovered in Australia, they need to turn to to a US or European company to turn it into a product. But that's more a consequence of poor industrial policy (most of Australia's pharmaceutical manufacturing sector moved overseas, and what's left is mostly lower-end stuff like vitamins and herbal supplements, with rare exceptions such as CSL) than anything to do with drug pricing.
[0] https://www.who.int/observatories/global-observatory-on-heal...