Apple News+ or whatever it is called does this. It has a good spread of papers across the country (Houston Chronical, LA Times, Kansas City Star, etc), but obviously doesn't include the bigger publications like the NYTimes or Washington Post.
I was seriously looking into Apple News+ a few months ago, but it turns out you have to use the app (from what I remember), which of course requires an Apple device.
I only have an iPhone, and like to read news on my computer or tablet which doesn't run iOS. So that's a no-go for me :/
