Would that they did, but not every news page on the Web has an RSS feed. If you want to be able to use your RSS reader to follow a feedless page, try FeedYes.com. Type in the URL of the page, and it creates an RSS feed for the page.
FeedYes claims to work with most Web sites (except those built in Flash). I had trouble with some pages I tried, but others worked fine. It seems to require that the Web page be a news page of some sort, with some minimum of contextual links. It also allows you to tag the feeds you create.