Because Outbrain and Taboola can easily be 1/10th or more of a legit site's revenue, on the order of millions of dollars. I'm not saying that's a good thing, it's a very difficult argument with the amount of money you could potentially miss out on.
I may place less importance on “brand coherency” and more on “value to myself” than others.
The damage to their reputations may cost substantially more in the long run. Doesn't take many "I clicked a NYT article and it was a scam" experiences to permanently sour someone on the outlet.