If you pay with your data instead of money, how does that make a service "free"? It would only be free if your data was worthless. But then they would not collect it in the first place.
Absolutely, those are entirely different. But you do seem to be defining "providing a service" as not-paying. If you go down that route, why do houses cost money? You are paying the builders for their service, but if that's not-paying, then you're just giving away huge sums of money for zero value in return. Tangibility isn't a defining line, or utility companies would be out (they don't provide water, they bring it to you. An intangible service.).
The service in these cases being fewer "enlarge your breasts/penis" ads for the wrong sex, or anything you may find offensive, replaced by ads which (ideally) would help you discover things you want which you may not have found otherwise. You're paying the ad services to be your personal product investigators, and they return value by providing relevancy.
edited to add more. I'm done now!