I think the demographics that just use the default search engine are probably most desirable for the advertising publisher as they are more likely to click on ads.
Advertisers aren't looking for the most likely to click, they are looking for the most likely to convert. Clicks cost money so they only want to pay for people that are highly targeted. This is why search advertising is so powerful, it is about matching the intent of the user (their search terms) to products and services, and getting them at the right time (when they are open to new paths).
Search ads are powerful for targeting users, but branding requires FB kind of ads.