Some non-legacy news sites do make ads first-party content, i.e. native advertising or sponsored content. BuzzFeed is probably the most prolific at it [0], with a great tech team and focus, but even BuzzFeed is floundering when it comes to revenue targets. I think Quartz [1] also does it well (though it's also part of the Atlantic media group. Newer outlets do it well too -- e.g. theoutline.com and axios.com -- but both are too new to know how viable their business is.
Of the legacy outlets, New York Times is in the forefront as it is in most digital categories (the creators of D3, Backbone, and other tech have been on the payroll), but most of their gains seem to have come from digital subscriptions, with digital advertising still nowhere close to offsetting the loss in print ad revenue [2]
I'm guessing the reason why native advertising hasn't been the status quo is related to inertia and the timing of seismic change in the industry. When I was in j-school many years ago, the professors were fond of saying that newspapers was basically money printers with profit margins only rivaled by the cocaine trade -- though this was only the case after TV and radio crushed the industry, to the point that most cities became one-newspaper monopolies.
At around the time of the digital boom, i.e. 90s and mid-200s, regional and local newspapers were floundering and bigger players figured it be wise to swoop them up and turn one-city monopolies into regional monopolies. The NYT famously bought the Boston Globe in 1993 for $1.1 billion -- and then sold it for $70m in 2013 [3]. McClatchy had become the 3rd biggest publisher after buying the Knight-Ridder chain for $4.5 billion in 2006 [4] and racking up $2B in debt as the entire industry was facing double digit drops in revenue. And all of this was about the time when publishers realized (too late) that Craigslist had effectively decimated everyone: classified ads were once as much as 20-25% of a newspaper's revenue. All this is to say that the news business definitely had the money to blow on innovation [5], but by the time they realized how fucked the Internet was going to make things, they weren't in a position of confidence and stability. There was some efforts -- I think cars.com was a bright spot for McClatchy and Tribune [6] -- but all too little and too late.
The shitty ads that I see news sites serving up seem to me to be a symptom of legacy inertia and existential panic -- going with DoubleClick and other shitty 3rd-party ads probably seemed like the most efficient solution. Remember that most of these companies still have significant print ad departments, because these ads still make way more money than digital. And then there's the traditional firewall between the editorial and ad departments. I worked at a McClatchy newspaper as a reporter and a developer and there were many problems arising from the fact that digital operations were basically under the business side, and effectively in an entirely different building.
I think the other problem is that ads are fundamentally a different experience in print than they are on the web (and for TV and radio). Newspapers have a whole page to work with for ad layout, and ads can come in all kinds of sizes and formats, from full-page ads to small bottom corner ads to tiny classifieds. When newspapers were rolling in money, they were also the primary places for the average citizen to find out things like stock prices, government auctions/notices, apartment rentals, and local sales and events. My parents (Vietnamese refugees) weren't much into reading English publications, but we subscribed to the local newspaper's weekend edition because it was chock full of ads and coupons. Ads were a destination -- arguably, for the average person, they were more valuable and desired than the newspaper's actual editorial content, in the way that people might watch the Super Bowl just for the ads.
In today's web environment, is there any normal mindset in which people actively seek out ads (other than looking them up on YouTube if you missed the Super Bowl)? The kind of native advertising that BuzzFeed et. al seem to have the most success with are advertorials that don't seem like ads. Unfortunately, this creates its own conflict with news-minded organizations.
[0] https://techcrunch.com/2014/08/12/buzzhome/
[1] https://nypost.com/2017/11/16/buzzfeeds-revenue-to-fall-70m-...
[2] https://www.nytimes.com/2017/11/01/business/media/new-york-t...
[3] http://www.nytimes.com/2013/08/04/business/media/new-york-ti...
[4] http://www.nytimes.com/2008/12/06/business/media/06paper.htm...
[5] http://archives.cjr.org/feature/the_newspaper_that_almost_se...
[6] http://www.chicagotribune.com/business/ct-cars-spinoff-0908-...