Tons of comments here confidently say that the very idea of targeting clearly doesn't work based on their own experience or that it's a house of mirrors that doesn't work because of some obscure math.
I've managed over $10 million of ROI focused ad spend on Facebook and Adwords. You can test if targeting works trivially:
1) Use the platforms to target one audience that's a generic "All US Population" audience.
2) Test this against (for example) an algorithmically generated Lookalike that FB creates based on your seed audience.
The Lookalike will generally perform 3-20x better than the general population, depending on how specific the audience is your trying to target.
As far as public data goes, 90% of new ad spend goes to FB and Google for a reason - they're the best ways of targeting specific audiences online. And this is easily provable if you've ever worked on even mid-size ad campaign.
Buying ads on the NYT Health section is a form of targeting. It's also a much lower noise targeting compared to programmatic.
I'll also note there's very little scale in direct ad buying - very few niches have scale that matters for any audience smaller than "interested in business". That said, programmatic outside of FB and Google is indeed trash and the NYtimes did well to drop it. But pretty much everyone in the thread conflates Facebook and Google (Again, 90% of spend) with the 1000s of random ad tech firms out there of dubious quality.
EDIT: and the downvotes begin, at this point it's just comical.