People have been claiming newspapers are obsolete in some shape or form for 50 years, ever since television became everyone's primary method for keeping up with the news. In practice, newspapers, while hit, never went away, while TV news has become supplanted by the Internet.
And who is dominating news on the Internet? Oh, yeah, the newspapers. Most of us have at least one newspaper's website that's on our rotation of sites to check every day, despite the attempts to get us to use news apps or search engine news aggregators - both of which suffer in that they mix the latest from, say, the Daily Mail, with that of The Guardian or Washington Post.
As for this:
Few people spend the time to read the entire article when they are looking for headlines and sound bites
Few do, But few have ever done. You think, if you teleported back to a New York Subway car in the 1940s, every strap hanger was reading the New York Times on the way to work? Go to a London Underground Tube Train in the 1950s, and every passenger was reading The Times, Guardian, or Telegraph?
There's always been a range of newspapers providing news in different formats for different readers, and the most popular have always been the ones screaming headlines that today we'd call "clickbait", and whose articles are scarcely a few sentences long.
The New York Times is an exception, because it caters for the market of people who want more. It's always been a small minority that reads it. The difference between the days of paper and today are that all of a sudden the NYT can have an engaged audience that spreads far beyond the range a printed, time critical, newspaper can be delivered within, and that without page limits, its no longer limited to coverage of the region it serves.
Which is why the New York Times is doing very well right now, when 20 years ago it wasn't.