I think some of the reason Google News is the way it is has to do with balancing the line between providing free content and not paying copyright holders (Newspapers). Someone please correct me if I'm wrong.
That being said, you're correct about quality being an issue. It seems that there are more algorithms, and less human component, deciding what reaches the front page. I think it would work better if it were like this:
1) Algorithm "bubbles up" the best news stories.
2) A trained human (or humans) filters through them, selects the best article.
3) Said article gets posted on the front page.
The trained person would have to have good journalistic taste. Pick out articles with proper headlines, rather than link-bait titles, or titles written by someone who has little clue what he/she is talking about (e.g. there aren't many journalists who are DBA's).
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A BIGGER problem is this: Showing only "news" and not "fluff".
Whenever there's a top-ten list, celebrity news, an op-ed piece, sports "news", reports on "marketing material" for new products/services, a puppy who fell down the well, "sharks" in the ocean (who pose no threat to you), the virgin mary appearing on a piece of toast, etc..., that's not real news. That's entertainment.
It would be nice if there was a news source that filtered all of that crap out. It might be as simple as gathering all news stories, and RegEx'ing out anything that also appears on Fark.com. ;)
The only news organization I'm aware of which does this well is PBS's News Hour. The problem is their presentation is very dry. On the plus side, they don't have "opinionated" reporters who add judgmental tones of voice and facial expressions to their presentation.
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Another random thought goes back to Op-Ed pieces. It would be nice if all online newspapers, or some sort of services, marked them as such, visually distinguishing them from news pieces. Perhaps make the webpage background light sky blue, rather than white. Anything, in a subtle visual manner, which states "This is someone's opinion; it may or may not be true".