Was this someone's job?

Yes. In fact there were whole companies who provided what was called a "clippings service." You basically subscribed to their service, and told them what you wanted news clippings on. They would watch for articles related to that subject/person/whatever to come up in the newspaper, and then send you all of the clippings that they'd accumulated periodically.

Not all of the "clippings files" that are out there were generated by clippings services though - some institutions (state and local libraries are the big ones that I know of) sometimes used to buy multiple copies of local/national papers every day, cut them up and file articles of local/historical interest by subject. These tend to be a bit more hit-and-miss in terms of their coverage, though, because the process of clipping and sorting the articles wasn't quite as consistent as a commercial clipping service.

It still exists as a job. Media monitoring firms provide articles, clips etc, to business and Govt on the basis of specified subjects for a fee.