Wishbone
Paladin Radmaster
No, it has not "been proven" that we are unable to persuade people to change their minds about important topics of the day. It's often difficult to do, and even more difficult to do it with the impersonal medium of the internet, but science hasn't "proven" that persuasion is not possible.
But more on point, changing the minds of the speaker we disagree with is not the point of the marketplace of ideas. The marketplace of ideas is that the best opinion wins out with the audience at large - not with the person we're dissenting from. The goal of spreading good speech to counter bad speech is to persuade other listeners, not the person making the bad speech.
Williams Jennings Bryan and Clarence Darrow were not trying to persuade each other concerning their views on creation versus evolution. Ultimately, they were trying to persuade the public at large. That's the marketplace of ideas in action. And it does work.
So since there's been broader adoption of many of the ideas put forward by protest movements it follows they're selling something most people are buying into in the marketplace, no?