It's still free. You choose to access an API, whatever that may be. You don't get to decide what the format is and you don't get to decide what the content (the ads are content in the HTML) is.
> The assumption that the only way for websites to make money is via ads or paywalls is completely pervasive and it's simply not true.
You are lumping all websites together, which is unhelpful. A tumblr page vs Apple.com. How you measure profitable is not cut and dry. Google's search isn't profitable, but the reselling of data and injection of data side is. Just because you have an agenda, doesn't mean the ecosystem matches your ideal wishes. The internet itself transmits VAST (pun!) amounts of data and ads are a small portion of that compared to say...video. 300 Hours of Video Uploaded to YouTube Every Minute. How much of that are ads? It's about 2 hours. The internet is not expensive because of ads. They sit nicely on top of it, which is part of why they are tolerated.