But as far as I can tell, there is nothing about newspapers that makes them a natural monopoly. Why should anyone regulate combinations in that area?
Very, very few regulations are designed with the sole purpose of dealing with natural monopoly. Most are there to prevent some monstrous or dystopian consequence of unfettered capitalism that we as a society have decided is undesirable.
Having a tiny group of wealthy oligarchs own all media, press, acceptable thought in an area is one of those horrifying dystopian consequences that we apply these regulations to prevent.
Be careful any time you see an analysis of media consolidation that ignores the reality on the ground -- the media's unique ability to define and shape public opinion. Such an analysis is either so purely academic as to be not relevant to any actual political or social discussion, hopelessly naive or, worse, willfully ignorant in service of a particular ideology.
When regulations aren’t designed to address identifiable market failure modes, like for example a natural monopoly or negative externality, they’re usually driven by vague public interest handwaving. Economic theory is hardly infallible, but it’s a lot better of a basis for law than that.
While I can't provide theory, in practice they certainly are. Every city has one or two papers of any significance; it's hard to name a new major newspaper that started in the last 50 years. In many places, the leading papers have combined for economic survival, but kept their editorial pages separate, for diversity of voices.
Maybe it's due to high barriers to entry? You need a printing press, distribution, and a reputation for reliability - the last probably being a newspaper's most valuable, irreplaceable asset.
The Internet provides more competition and lower barriers to entry, but I'll bet the leading Internet news source almost every town is the local newspaper(s).
Producing a newspaper of a certain number of pages of a certain quality requires the same amount of work, regardless of whether it is read by 10 people or 10 million, but your revenue will be proportional to readership; you have a small per-reader additional cost, to print or provide bandwidth, but it's largely a fixed cost, to research and write the articles.
I'm not sure how the internet helps or hurts. It will help in that you can start smaller on the internet, with a one or two person operation publishing infrequently, but when you try to scale up you'll run headlong into the "people don't pay for news online" problem.
In any case, if you want to run a "real" newspaper, you need a certain minimum number of subscribers to be viable, to hire enough people to research enough articles to provide enough information each day to really be considered a "newspaper". This, in turn, is where you could imagine unfair competition from monopolies. First, your larger newspapers will be able to undercut you, producing better news articles at lower cost per reader, if they have more readers. Second, a large enough conglomerate of regional newspapers can afford to run some at a loss. There are only so many available subscribers, and if you can deny your competitors enough to be viable, they'll also be running at a loss, and your deeper pockets will let you wait them out.
Not yet, but as local newspapers continue to lose readership to the internet, the will start consolidating and/or failing. After say 20 years of this, there will be only the big online national papers, NYT, WaPo and some others that serve a large niche. There will always be room for the smaller niche papers though.