Where did you get this idea that free speech would solve all problems of ignorance? Perhaps you could stamp out at least public displays of climate change denial or anti-vaccine messages, but then you'd also stamp out criticism of the government and any narratives that challenge the corporate power structure, whether true or not. It's obvious that lies would be worse if free speech were restricted, as evidenced by the many countries that have restricted it.

In any case, the idea of free speech is explicitly to support unpopular forms of speech. Challenges to the status quo are intentional, whether informed or ignorant.