What's stopping Google from refusing to pay the news sites, thus de-indexing them from Google entirely? If the relationship is "pay me for my content", then refusing to serve links to their media is absolutely within their rights. Only the publishers have something to lose here.
The next step is probably a version of "must carry" for the Internet where Google is required by law to index news and required by law to pay for it.
A "news website" and "news agregator" are... what exactly? Since search traffic is so valuable, publishers would modify their sites readily to fall just under the legal threshold for news sites in order to get picked up by Google's non-aggregator of non-news sites. It's virtually impossible to craft definitions that are simultaneously not trivial to circumvent by Google and also have no impact on established, unrelated internet content.