Most free web sites pay for their upkeep with ads. It has been an unwritten agreement since forever (or at least as long as there have been ads on the web) that if you consume the content, you pay the creator by looking at the ads on their site.
Consuming the content without looking at the ads is like shoplifting because you don’t like the way a store’s checkout counter works and/or the fact that they want money from you at all.
They may grab your payment info though, and use it to build a profile of you that tracks your spending habits to share with others.
Source: was one of the people whose cards had been compromised by the massive data breach Target had about a decade or so ago, because Target had been saving payment information on every customer to build profiles from.
Now I think the newer chip-based cards and tap to pay have made it harder to track customers, but that’s basically why every company is trying to push its own app these days.