I think we'll just reach a point where the public will be so knowledgeable of fake news that unless AI doesn't debunk it, people just won't pay attention to it. I might be assuming the general public is much smarter than it is, however.

In my dream world that would be the case. In real life, unfortunately, it is not. How many people don't even read beyond the headline? Fake news are rampant and the people who are sharing them are real people. They could be your family, relatives, friends, or colleagues. These people are aware that there are fake news especially in social media and yet there are still many who still share them and talk about them as if they were really real. They believe them most of all if its support their bias or whoever they are following, like a politician or a celebrity.
So if AI can create fake news, then AI should also be able to detect and remove them. We just have to actually trust that the people behind them are actually doing it for the general good and not for their own.
I merited this, but I have to make clear that I don't agree on the last sentence. You can't trust the group of people creating AI because there are lots of individuals with different goals, limited capacities etc. And AI is already creating more AI.