The primary problem you have is that your site is nearly completely dynamic and likely completely changes daily. This means that Google is seeing a different website every time it visits. Of course I am going to assume that some of the articles remain for a period. I cannot tell. Without seeing your site, I have to make many assumptions and work from these assumptions.
You have to look at things from Google's point of view.
Google will re-fetch often any page with a shorter TTL time meaning that the page changes often and gives more weight to these pages and keywords as being fresh and short-tail.
Google will see any article pages with a slightly longer TTL time and weigh the pages and keywords as slightly more long-tail but still fresh.
Google will find that all of the TTL times are short for most pages and will look for pages with TTL times within normal ranges and assume they are important.
That most pages are relatively temporary in nature and that any page that remains must be important to the site and will be weighted for long-tail keywords.
When using site:domainname.tld, Google lists the pages by importance which has absolutely nothing to do with search and search engine result page(s) SERP(s) except for the one factor importance is amongst the many that Google uses to return results. While I do a site: search from time to time, I know that the results are only an indication of what pages Google deems important at the time. However, if I do a general search for my keywords, things change. Here is where I find out how my search terms really perform and what pages bubble to the top. These are two different things. The latter being vital and the former being insignificant in the real scheme of things.
You have to remember that searches on any search engine changes daily especially for news. There is rarely anything long-term about search within your industry except for searches for archived articles.
For any dynamic site such as your seems to be, the important pages are likely to be longer standing pages with search/results(impressions)/click-through rates/history metrics that make the page important. These are the things that search engines measure to know what pages are important. Pages that appear and disappear will not have metrics enough to rise it to the top of a site: search. For pages that change often, the keywords/impressions/click-through rates will vary depending upon the popularity of the search terms used to find the page. And since we know that searches change daily, this will change daily.
I am not sure of what you are seeing and the concerns you have. I cannot evaluate your site to know what may be going on. However, I hoped that I explained things well enough that you get the picture. Do not mistake a site: search as being akin to any search performance indicator. It only illustrates one of many factors that go into how a site performs and should not be used as an indication for SEO purposes too much. Do not let it confuse you.