Simple answer to this one: Some papers did try to charge for access early on. But users soon realized that the National news was just that, National. They could get that anywhere. And most (not all of course) local news is just fluff to fill the pages. Some sites still have a premium section for fee but I can't imagine that they make much cash on this.

What will be missed if too many go under is the quality investigative reporting that goes on to keep local governments etc. in check.

If case you haven't seen this site: http://www.newseum.org/todaysfrontpages/flash/

It is a good starting point for the front page of almost every paper in the USA. From there you can go to their web site (if any) for more in depth coverage.