In the analogy (and online), the newspaper with blank spaces (aka the ad-supported site) is a small and insignificant data player. It's mostly advertisers that are collecting and retaining the data, and not just on websites but in all kinds of ways. The profiles are kept by advertisers, and sold on data exchanges, completely out of the reach and control of the ad-supported site. So unfortunately, ad-supported sites that offer up their ad inventory via real-time bidding can't provide the information you'd want. You would really need to opt-in at every point where data is collected, which is everywhere.