They're popular with people who take the subway. Think about it, you're sitting there for half an hour with no service. An app that pre-downloads all of a newspaper's stories is handy and easy to use.
There's an advantage to Instapaper and company in that it's centralized and you only have to launch the one app to pull down all of your content regardless of the source.
And here I thought in 2013 apps could download their content in background when phone is idle. Maybe when the owner is sleeping at home with fast wifi all around. Might make too much sense though.
iOS does not allow background downloading, unless your app is part of Newsstand. While it would seem to make sense to make your news delivery app appear in Newsstand, it does come with some trade-offs, most significantly that your app is locked inside the Newsstand shelf and can't be placed in a primary app slot.
And, even if your app is in Newsstand, you have to actively go into Settings and turn on background download on an app-by-app basis.
Finally, even then, the app will only background-download if you're on a WiFi connection. I agree, this makes sense in this age of metered WAN bandwidth.
So, if you're using iOS, there's a really good chance that you will not have that content before getting on the subway, unless you remember to click into it on the walk over to the station.
In principle, you're exactly right -- but iOS in particular has been notoriously picky about app sandboxing, and there is a very short list of permissions that apps are allowed to ask for: location, push notification, and I believe now address book access.
(Okay, you could use Skype or whatever, but I'd expect the latency and reliability of the connection is too shitty for that.)