Many US newspapers now redirect to tronc.com for a standard disclaimer.

For example, the LA Times redirects to http://www.tronc.com/gdpr/latimes.com/, which says this.

Unfortunately, our website is currently unavailable in most European countries. We are engaged on the issue and committed to looking at options that support our full range of digital offerings to the EU market. We continue to identify technical compliance solutions that will provide all readers with our award-winning journalism.

The Frederick News Post of Frederick, Maryland does this.

https://www.fredericknewspost.com/

Whats happening in real i think is that EU realized it will never be able to chop Google or Facebook in pieces so they make it harder for these companies to exist on local market. At the end of the day free market still rules in Europe - if Facebook disappears their hole will be quickly filled in with 20 other social networks “made in European Union”.

Mark my words: if this were enforced, people and most companies would simply stop linking these sites. What I think will happen instead is that many websites would not want this kind of situation, so we will add a new clause to the robots.txt permitting linking and small snippets, and most websites would enable it rather than lose the link and search traffic. Then we'd be back where we started.

By the way, what happens when an European newspaper is hosted in US? What laws apply?

Maybe search engines could adopt some sort of standard that would allow pages to provide their desired description using meta tags if they don't want an automated summary. I could see a problem with pages using dishonest summaries, but perhaps that could be addressed by penalizing the page rank if the provided summary is too different than the summary that Google would have generated.