They could, but then only those two paragraphs would be indexed. That would make the content less rich, less relevant, so it wouldn't rank as high.
That's for the normal organic search results. I don't know the policy for showing up in Google news and the carousel. I suspect it wouldn't be allowed.
Edit: You can be subscription-only and be in Google news, but you have to show the same limited snippet to both Google and end users. And you get 'tagged' in the UI as subscription only. https://support.google.com/news/publisher/answer/40543?hl=en
That's for the normal organic search results. I don't know the policy for showing up in Google news and the carousel. I suspect it wouldn't be allowed.
Edit: You can be subscription-only and be in Google news, but you have to show the same limited snippet to both Google and end users. And you get 'tagged' in the UI as subscription only. https://support.google.com/news/publisher/answer/40543?hl=en