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.