I rather like the solution the Apple/Google have come up with because it solves a more general problem very nicely. The more general problem is "malware" for what of a better word (it's perhaps too harsh) - apps that lie or mislead about what they do and hide what their bluetooth proximity harvesting in the permission thicket (who here would automatically associate the "Fine Location" permission with bluetooth proximity harvesting).
But notice in this particular instance that's not what's happening. There is no attempt to deceive. The app is purely opt-in, and what you are opting into is very explicit. In this particular case there is almost no difference between what Apple/Google propose and TraceTogether. The difference amounts to when you give the government permission to know who you are. For TraceTogether it happens when you install the app. For the Apple/Google proposal, it's when you see your doctor when being notified you are infected. In both cases, no privacy is given up until you are infected, and assuming you installed the app in good faith and do get tested when notified the outcome is the same.
There is the minor problem the Australian government could surreptitiously change the app to something more sinister down the track. I'd be very confident they would not do it now, but 24 months later when attitudes reverted it's sadly entirely plausible. That could be fixed by changing release policies (such as publish source before deploying). But it looks like for whatever reason they won't be doing that, so perhaps Apple/Google forcing them deal with the citizens they govern honestly and transparently is a good thing, despite the delays it causes.
I saw a tweet yesterday about having to leave the screen on, but it turns out the source website was updated to remove that line, and that's not how the app works. However, there are also screenshots on Twitter of lock screen notifications saying that the app needs to be open so I don't know any more...