What about the Netflix/Spotify model? Pay a monthly subscription for "premium news" and then let the content providers divvy up the monies based on pageviews.

That would simply accelerate existing trends. All the money would go toward pumping out more celebrity gossip because that's what gets eyeballs. There would be no remaining incentive to engage in actual journalism.

Profit-based news is irretrievably broken.

There's nothing wrong with profit news. That is how all news generally works - journalists generally don't work for free. However they should rely on adverts like the other online news sources.

Journalists get paid, that doesn't mean the news organization that pays them must be a for-profit entity.