No, it wouldn't. the aggregation google gives is a bonus to the companies being aggregated. Why should it pay any money for it? It's like a guidebook company having to pay the people it recommends.
TBH, they do have one argument - they supply content for Google and other aggregators to show. It raises an interesting question - at which point an ad becomes worthwhile content in and of itself?
For a more convincing scenario, some types of video entertainment are often considered glorified ads for physical merch, yet often they aren't free either, even if made at a loss.
But as i said, ultimately this is something that should and technically can be settled through negotiation, rather than government intervention - they are free to erect paywalls so that aggregators can't mooch off links to them, as some more respected, usually specialist publications already do, but as their own decisionmaking shows, it would hurt them more than it would pressure the aggregators to share their revenue... because their content apparently is not good enough to convince much audience to pay for it, so being free content for aggregators and an ad to drive people to the publisher's site is probably more worthwhile for them - the aggregator's audience seeing normal ads on the publication's site which the publisher will be paid for is the most use this content has, according to what we can see.
So they want to go around the whole annoying market, competition and negotiation stuff and have the heavy hand of government grant them a victory so decisive that they couldn't possibly achieve it in negotiation.
Google isn't handling it the best though - in their place, instead of threatening full to remove services from Australia right away, i would just publish an open letter to the point that any of Australia's news outlets that feel exploited and cheated out of their rightful revenue by Google are free to send one email request, and any links to their site will be forever blacklisted from Google's search and aggregation services, so that such exploitation won't continue. And then keep a monthly tally of how many publications took the offer.