You are wrong, though public interest is certainly the basis of the purpose of fair use doctrine. But the simplest way of demonstrating that fair use still allows commercialisation is probably this example: search engines absolutely depend on fair use if they include any content from the linked pages. (And some countries have even tried to call the act of linking copyright infringement, though they’ve tended to back off at least a little, to requiring at least the title or other content for it to be infringement, and not just the URL.)

https://en.wikipedia.org/wiki/Fair_use, lots of good reading there.