Historians, genealogists, etc. find it valuable to look at news reports from several hundred years ago. It's important to society for a prominent paper's articles to be archived somewhere independent of the news organization itself.
Plenty of libraries archive the Times. It still produces print and microfiche editions.
This is one of my biggest pet peeve's with a media. They will get something flat out wrong, stand beside it, and then much later go back and secretly change it without putting anything that it was changed. I would trust an Archived New York Times story over one that was in the NYT archives.
That's why I choose newspapers that provide a PDF version of their newspaper :)
I'm not sure what the outcome was but at some time Portugal's Expresso's archives were deleted by a cyberattack. At the time (never rechecked) I got the feeling the older articles were lost.